Elementary Algebra on Vedic Mathematics

Contributed by:

Harshdeep Singh Fri, Apr 08, 2022 01:33 PM UTC

This PDF contains :
Abstract,
Keywords,
Introduction,
Use of Vedic Formulas in Elementary Algebra,
Parāvartya Yojayet:
(i) Use of Paravartya Yojayet for algebraic division.
(ii) Use of Paravartya Yojayet formula to solve simple equations,
(iii) Use of Paravartya Yojayet formula for solving Simultaneous Equations,
(iv) Use of Paravartya Yojayet formula in Partial Fraction,

Sunyam Samyasamuccaye :
Meanings and Applications of Sunyam Samyasamuccaye.
Anurupye Sunyamanyat :
Antyayoreva :
Lopanasthapanabhyam:
(i) Use of Lopanasthapanabhyam for factorization,
(ii) Use of Lopanasthapanabhyam to find HCF

1. MEC
Print ISSN: 2645-8500
Elementary Algebra on Vedic Mathematics
Krishna Kanta Parajuli
Department of Mathematics, Valmeeki Campus, Nepal Sanskrit University
Email: [email protected]
Abstract
The South Asian region has a long history of discovering new ideas, ideologies,
and technologies. Since the Vedic period, the land has been known as a fertile place
for innovative discoveries. The Vedic technique used by Bharati Krishna Tirthaji is
unique among South Asian studies. The focus of this study was mostly on algebraic
topics, which are typically taught in our school level. The study also looked at how
Vedic Mathematics solves issues of elementary algebra using Vedic techniques
such as Paravartya Yojayet, Sunyam Samyasamuccaye, Anurupye Sunyamanyat,
Antyayoreva and Lopanasthapanabhyam. The comparison and discussion of the
Vedic with the conventional techniques indicate that the Vedic Mathematics and
its five unique formulas are more beneficial and realistic to those learners who are
experiencing problems with elementary level algebra utilizing conventional methods.
Keywords: Elementary Algebra, Paravartya Yojayet, Sunyam Samyasamuccaye,
Anurupye Sunyamanyat, Antyayoreva, Lopanasthapanabhyam
Introduction
The word ‘Algebra’ was originated from the corruption of the Arabic word
‘Al-jabar’al-muqabulah’ where ‘al’ means ‘the', ‘jabr’ refers to the operation of
transferring a quantity from one side of an equation to another while ‘muqabulah’
means the process of subtracting similar quantities from both sides of an equation
(Sidhu, 1990). Algebra is either a form of mathematics in which letters and symbols
are used to represent numbers or a generalization of arithmetic in which numbers are
represented by letters that are combined according to arithmetic rules (Hoad, 1996).
The numbers are often represented by the symbols called variables. Its concepts are
often required in teaching and learning to return to corresponding circumstances in
Arithmetic. As a generalized arithmetic, it can be linked to geometry by claiming
that algebra is only written geometry and geometry is only pictured algebra (Sidhu,
Generally speaking, algebra can be divided into two levels: elementary
and abstract. Elementary Algebra is the most fundamental part of algebra that
is commonly considered to be essential for any study of mathematics and
its applications, i.e., the part of algebra that is typically taught in elementary
mathematics courses (Cajori, 1919). The more abstract part of algebra is known as
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2. Elementary Algebra on Vedic Mathematics 83
Abstract Algebra or Modern Algebra which extends the familiar concepts found in
elementary algebra to more general concepts. Abstract Algebra or Modern Algebra
is mainly studied by trained mathematicians, and it involves the axiomatic definition
and investigation of algebraic structures such as Groups, Rings, and Fields (Menini
& Oystaeyen, 2017).
Algebra's origins can be traced back to the ancient Babylonians, who
developed it as an advanced arithmetical device. In the same period, the Egyptians,
Greeks, and Chinese formed linear and quadratic equations (Struik, 1987; Plofker,
Imhausen, Robson, & Dauben, 2007).
It is considered that, before 300 BC the Bijganit (बीजगणित) was derived from
the Bakhshali Manuscript (वाक्शाली लिपि) (Parajuli, 2021). At that time, the Bijganit
became one of the most influential practice and widely spread throughout the
continent. In pre-medieval era (500 BC – 400 AD) the development of Bijganit
took place rapidly as mathematicians were putting their hard and continuous effort
upon it. Further development of arithmetic and Bijganit took place in the later time
of the medieval era (400 AD – 1200 AD) which then got spread to Arab and other
countries. (Parajuli, 2021; Acharya, 2015; Boyer, 1991). Brahmagupta (598 AD –
668 AD) was a famous South-Asian mathematician and astronomer. He wrote the
method of solving linear and quadratic equations in his book Brahmasphutasiddhant
(ब्राह्म्स्फ़ुटसिद्धान्त) in 628 AD (Parajuli, 2021). It is greatly to the credit of Brahmagupta
that he gave all integral solutions of the linear Diophantine equation i.e., ax + by =
c, where a, b and c are constants (Boyer, 1991). Bhaskaracarya-II (1114 AD – 1993
AD) was the famous leading mathematician of ancient Indian during 12th century.
Bhaskaracarya wrote Algebra in his Siddhantasiromani (Patwardhan, Naimpally
& Singh, 2015). Hence, talking about the development of algebra, the South Asian
region has a long tradition of inventing new ideas, principles, and inventions. Since
the Vedic period, the land has been regarded as a fertile ground for new inventions
(Parajuli, 2021; Groza, 1968).
Many eastern and western mathematicians contributed to the modernization
of mathematics. They contributed to the subject of algebra as well as other areas
of mathematics. South Asian mathematicians have made a significant contribution
to these fields (Groza, 1968; Struik, 1987). Furthermore, Bharati Krishna Tirthaji
(1884 AD – 1960 AD), a South Asian glorious and divine human, made a significant
contribution to the development of mathematics in the nineteenth century (Tirthaji,
2015). He is well-known for rediscovering and reconstructing the new ideas of
mathematics from ancient Sanskrit text Veda early last century between 1911 – 1918
is popularly known today is Vedic Mathematics (Parajuli, 2021). The Vedic method,
he claims, is based on sixteen formulas and an equal number of sub-formulas that
cover all branches of mathematics, both pure and applied (Patwardhan, Naimpally &
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3. 84 K. K. Parajuli
Singh, 2015; Parajuli, 2021).
Out of two levels of algebra, abstract algebra and its problems are not
addressed in this article. This paper concentrated solely on the fundamental level
of algebra, which are generally required in elementary mathematics courses.
Furthermore, this paper focused on how Vedic Mathematics uses Vedic techniques
for effectively solving these levels of problems. There are two types of techniques in
Vedic Mathematics: specific and general. This paper consists of specific parts with
the Vedic formulas as Paravartya Yojayet -k/fjTo{+ of]ho]t\_, Sunyam Samyasamuccaye
-z"Go+ ;fDo;d'Rro]_, Anurupye Sunyamanyat -cfg'¿Ko] z"GodGot\_, Antyayoreva -GToof]/]j_
and Lopanasthapanabhyam -nf]k:yfkgfEofd\_ which are the most commonly used for
elementary algebraic solutions.
Use of Vedic Formulas in Elementary Algebra
Vedic Mathematics is a system of reasoning and mathematical working based
on ancient mathematical concept as well as modern concepts with precise unique
techniques based on its formulas with simple rules and principles (Parajuli, 2021;
Tirthaji, 2015). Many Vedic formulas can be used to solve algebraic problems. This
paper does not include all Vedic formulas. Only those that are appropriate for some
specific fundamental algebraic operations have been selected.
Parāvartya Yojayet (k/fjTo{+ of]ho]t)\
The literal meaning of the formula Paravartya Yojayet is “Transpose and
apply” (Tirthaji, 2015). This formula is used in algebraic division, solve simple
linear, quadratic, cubic equations, partial fractions of algebraic expressions etc.
(Parajuli, 2021; Tirthaji, 2015; Parajuli, Jha, Acharya, & Maske, 2020; Williams,
(i) Use of Paravartya Yojayet for algebraic division.
Let f(x) = a0 xn + a1 xn–1 + a2 xn–2 + … + an, (a0 ≠ 0). Let f(x) is divided by g(x),
then f(x) = Q(x). g(x) + R; where, Q(x) is quotient, R is remainder, f(x) is dividend
and g(x) is divisor.
In the illustrated figure below, the last row will formulate the quotient and
remainder pieces. The highest degree of Q(x) is equal to . The remainder (R) is
determined by the number of terms on g(x). If g(x) has m terms, the remainder
parts is taken from the right most m columns, and the quotient parts are taken from
the left most part. The path of arrows can be used to understand algebraic division
procedures, as seen in the illustration below (Tirthaji, 2015; Williams, 2019; Dave, et
al., 2018).
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4. Elementary Algebra on Vedic Mathematics 85
Division of 5x4 – 8x2 – 15x – 6 by x – 2 can be presented as follows.
x–2 5x4 + 0.x3 – 8x2 – 15x –6
2 5 0 –8 –15 –6
10 20 24 18
5 10 12 9 12
Here, Q(x) = 5x3 + 10x2 + 12x + 9; Remainder (R) = 12
The method is easily extended to the case where the divisor is a quadratic. For example,
the division x4 – x3 + x2 + 3x + 5 by x2 – x – 1 can be presented as follows.
x2 – x – 1 x4 – x3 + x2 + 3x +5
1 1 1 –1 1 3 5
1 1
0 0
2 2
1 0 2 5 7
∴ Quotient (Q) = x2 + 2 and Remainder (R) = 5x + 7.
(ii) Use of Paravartya Yojayet formula to solve simple equations
Paravartya formula can be used for special types of simple equations by merging
RHS into LHS under the different types of headings. If the sum of the numerators
2 5 7
on LHS is equal to the single numerator on RHS, for example + = i.e.,
x+3 x+4 x+2
N1(2) + N2(5) = N (7), then we apply the formula (where N1, N2 have their usual
meaning in Mathematics).
The merging procedure of RHS into LHS (Tirthaji, 2015; Parajuli, Jha, Acharya, &
Maskey, 2020; Parajuli, Jha, Acharya, & Maskey, 2019).
• For merging RHS into LHS, we subtract the independent part of denominators
of RHS from the independent part of denominators of LHS and multiply it to the
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5. 86 K. K. Parajuli
respective part of their numerators of LHS.
• As the work of merging has been completed, we put zero on RHS and by simple
cross-multiplication we obtain the result of x.
2 × (3 − 2) 5(4 − 2) −19
Therefore, + = 0 ⇒ 2 + 10 = 0 ⇒ x =
x+3 x+4 x+3 x+4 6
We use the same method for three terms as in two terms to merge the RHS of simple
1 3 5 9
equations if N1 + N2 + N3 of LHS = N of RHS. Consider + + =
x+2 x+3 x+5 x+4
1(2 − 4) 3(3 − 4) 5(5 − 4)
Here, N1 (1) + N2 (3) + N3 (5) = N (9). Then, + + =0
x+2 x+3 x+5
2 3 5 −5
i.e., + = . Again, using the formula as above, we get, x =
x+2 x+3 x+5 2
(iii) Use of Paravartya Yojayet formula for solving Simultaneous Equations
Paravartya Yojayet formula for solving simultaneous linear equations of general
form as a1 x + b1= y c 2 , which would be somewhat similar to Cramer's rule
y c1 ; a 2 x + b2=
(Tirthaji, 2015; Parajuli, Jha, Acharya, & Maskey, 2020). The cross-multiplication
method to solve simultaneous linear equation which is taught in our present-
day curriculum is also similar to the method Paravartya Yojayet (Tirthaji, 2015;
Williams, 2019). The Vedic formula moves in a cyclic order.
(iv) Use of Paravartya Yojayet formula in Partial Fraction (Tirthaji, 2015;
Williams, 2019).
To find the partial fractions of a proper rational function whose denominator is a
px 2 + qx + r
product of two or more linear factors. If we have to express in the
(x − a)(x − b)(x − c)
shape of partial fraction, then we write
px 2 + qx + r A B C
= + +
(x − a) (x − b) (x − c)
, where A, B and C are written as,
(x − a)(x − b)(x − c)
px 2 + qx + r px 2 + qx + r px 2 + qx + r
=A = ;B = ;C
(x − b)(x − c) (x − a)(x − c) (x − a)(x − b)
For getting the value of A:
• equate the denominator of A to zero, i.e. x – a = 0 ⇒ x = a
px 2 + qx + r
• put x = a in A =
(x − b)(x − c)
• we do similarly for B and C.
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6. Elementary Algebra on Vedic Mathematics 87
Sunyam Samyasamuccaye] (z"Go+ ;fDo;d'Rro])
In Sanskrit Sunnyam means zero, Sammye means equal and Samuccaye means total.
Therefore, the meaning of Sunyam Samyasamuccaye is when the Samuccaya is the
same, the Samuccaye is zero, i.e. it should be equated to zero. The word Samuccaya
has several meanings in different context. This formula is used to solve linear
equations, special type of quadratic equations, rational expressions, cubic expressions
etc. (Tirthaji, 2015; Williams, 2019; Parajuli, 2019).
Meanings and Applications of Sunyam Samyasamuccaye: The meaning and its
corresponding applications of the formula can be expressed as follows.
(i) When Samuccaye is a common factor of unknown quantities in all the terms of
linear equation then equate that factor to zero (Parajuli, 2021; Williams, 2019;
Parajuli, Jha, Acharya, & Maskey, 2019).
When 5 (x – 4) + 8 (x – 4) = 3 (x – 4) – 7 (x – 4), where (x – 4) is a common
factor, so x = 4 is the solution.
(ii) When Samuccaye is the product of independent terms in the expression like
(x + a) (x + b) = (x + c) (x + d) such that ab = cd, then equate the variable to
zero (Parajuli, 2021; Tirthaji, 2015; Parajuli, Jha, Acharya, & Maskey, 2019).
(iii) When Samuccaye is the sum of the denominators of two fractions having the
same numerator then equate the sum of the denominators to zero (Parajuli,
2021; Tirthaji, 2015; Parajuli, Jha, Acharya, & Maskey, 2019). When
p p
+ = 0 ( where, p ≠ 0 ) , then the solution is obtained by (ax + b) + (cx + d) = 0
ax + b cx + d
(iv) When Samuccaye is the sum of the numerators or denominators of the
expression like:
ax + b ax + c
= where, sum of the numerators (N1+N2) = sum of the
ax + c ax + b
denominators (D1+D2)
then the value of x is obtained by equate them to zero (Tirthaji, 2015; Parajuli,
Jha, Acharya, & Maskey, 2019).
(v) When the Samuccaye is the sum of the numerators or denominators/difference
ax + b cx + d
of numerator and denominator of the expression like: =
cx + d ax + b
where, N1 + N2 = D1 + D2 = 0, gives the 1st root of the equation
and N1 – D1 = – (N2 – D2) = 0, gives the 2nd root of the equation (Parajuli,
2021; Williams, 2019; Parajuli, Jha, Acharya, & Maskey, 2019).
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7. 88 K. K. Parajuli
When the sum-total of denominator on LHS and RHS are same (having same
numerator), then the sum-total equate to zero (Parajuli, 2021; Parajuli, Jha,
Acharya, & Maskey, 2019). For example,
1 1 1 1 1 1 1 1
when − = − i.e., + = +
x−b x−b−d x−c+d x−c x−b x−c x−c+d x−b−d
b+c
where, D1 + D2 = D3 + D4 = 2x – b – c. Then, 2x – b – c = 0 ⇒ x =
2
(vi) The expression of the form 3x − 8 + 4x − 35 =2x − 9 + 5x − 34 can be reduced to
1 1 1 1 x −3 x −9 x −5 x−7
+ = + . So, can be applied (vi)th application (Parajuli,
x −3 x −9 x −5 x−7
2021; Parajuli, Jha, Acharya, & Maskey, 2019).
Anurupye Sunyamanyat (cfg'¿Ko] z"GodGot\)
The meaning of Anurupye Sunyamanyat is “If one is in ratio, the other one
is zero”. This formula is used to solve particular type of simultaneous linear and
quadratic equations. If the ratio of coefficients of one variable is equal to the ratio of
their corresponding independent terms of the equation, then another variable is zero
(Parajuli, 2021; Tirthaji, 2015; Williams, 2019).
Consider the simultaneous linear equations of two variables: 6x + 7y = 12; 5x + 21y = 10
6 12
Here, ratio of coefficient of x = Ratio of independent terms i.e., =
5 10
∴ y = 0 then x = 2.
Consider the simultaneous equations of three variables as follows.
ax + by + cz = cm … (i)
ax + ay + fz = fm … (ii)
mx + py + qz = qm … (iii)
Here, ratio of coefficient z = Ratio of their independent terms
∴ x = 0 & y = 0 then z = m.
Antyayoreva (cGToof]/]j)
The meaning of Antyayoreva is "only the last terms". i.e. while applying the
formula, last two digits i.e. unit place and tenth place digit are observed (Tirthaji,
2015). This formula is used to solve the specific types of rational expression. The
specific type means: the type of equation of those whose numerator and denominator
on the LHS bearing the independent terms stands in the same ratio to each other
as the entire numerator and the entire denominator of the RHS stand to each other
x 2 + 3x + 6 x+3
(Parajuli, 2021; Tirthaji, 2015; Bose, 2014). Consider = where,
x 2 + 5x + 5 x+5
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8. Elementary Algebra on Vedic Mathematics 89
x 2 + 3x x(x + 3) x + 3
= = = RHS, which satisfies the condition of the Antyayoreva. So,
x 2 + 5x x(x + 5) x + 5
x+3 6 , i.e., x = –15.
=
x+5 5
Lopanasthapanabhyam (nf]kg:yfkgfEofd\)
The meaning of 'Lopanasthapanabhyam' is 'By alternate elimination and
retention'. This formula is used for factorization of 2nd degree homogeneous and
non-homogeneous polynomial functions with three or more variables. It is used
for finding HCF. It is also used in solving simultaneous equations, quadratic, cubic
equations etc. (Parajuli, 2021; Tirthaji, 2015; Williams, 2019).
(i) Use of Lopanasthapanabhyam for factorization
Specially, this formula is used for factorization of 2nd degree (homogenous and non-
homogeneous) polynomials in three or more variables. Therefore, it is an important
process to find the value of any variable which removes the difficulty of factorization
and make the factorization simple. Consider the polynomial of ax2 + by2 + cz2 +
dxy + eyz + fzx, which is homogeneous of second degree in three variables x, y, z
(Tirthaji, 2015; Williams, 2019).
For the factorization, we should apply the following steps as mentioned below
(Parajuli, 2021; Tirthaji, 2015; Glover, 2013).
• Eliminate z by putting z = 0 and retain two variables x and y. Factorize the
obtained polynomial using Adyamadyena (another Vedic formula) formula.
• Similarly, eliminate y by putting y = 0 and retain x and z and factorize the
obtained polynomial.
• With these two sets of factors, fill in the gaps caused by elimination process of z
and y respectively for finding the final factors of the original expression.
Consider the homogeneous polynomial, 3x2 + y2- 4xy – yz – 2z² - zx
Putting z = 0 gives the factors (x – y) (3x – y) and putting y = 0 gives (x – z) (3x + 2z)
By filling the gaps = (x – y – z) (3x – y + 2z)
∴ 3x² + y² – 4xy – yz – 2z² – zx = (x – y – z) (3x – y + 2z)
Consider the second-degree non-homogeneous polynomial
3x² + 6y² + 2z² + 11xy + 7xz + 7yz + 16x + 20y + 12z + 16
For non-homogeneous second-degree polynomial, we eliminate two variables
at a time and retain only one variable and the independent term, each time. Then we
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9. 90 K. K. Parajuli
obtain the result as described in the above steps. (We need one step more than the
homogenous cases)
Putting x = 0 and y = 0 gives the factors (z + 4) (2z + 4); putting y = 0 and z = 0 yields
(x + 4) (3x + 4); putting x = 0 and z = 0 yields (y + 2) (6y + 8) = (2y + 4) (3y + 4).
By filling the gaps: (x + 3y + 2z + 4) (3x + 2y + z + 4)
∴ 3x² + 6y² + 2z² + 11xy + 7xz + 7yz + 16x + 20y + 12z + 16
= (x + 3y + 2z + 4) (3x + 2y + z + 4).
(ii) Use of Lopanasthapanabhyam to find HCF: (Parajul, 2021; Tirthaji, 2015;
Williams, 2019; William, 2019)
Vedic Mathematics used the method elimination and retention to find HCF. In this
method, we divide through by factors continues until the remaining numbers are co-
prime as explained the following examples. By this method, we eliminate highest
power and lowest power of the given expression by adding or subtracting the given
expression from each other. We find the HCF by removing the common factor if any
from each (Parajuli, 2021; Tirthaji, 2015). For illustration, we find the HCF of the
expressions x³ – 3x² – 4x + 12 & x³ – 7x² + 16x – 12.
In addition, and subtraction columns, we should use the following steps as follows.
Adding Subtracting
x³ – 3x² – 4x + 12 x³ – 3x² – 4x + 12
x³ – 7x² + 16x – 12 x² – 7x² + 16x – 12
– + – +
2x³ – 10x² + 12x 4x² – 20x + 24
2x (x² – 5x + 6) 4(x² – 5x + 6)
(x² – 5x + 6) (x² – 5x + 6)
∴ HCF = (x² – 5x + 6)
Discussions
The illustration of Vedic formulas in the above sub-topic 2.0 is only confined
to a small portion of basic algebraic issues. The paper expresses how it can be
expanded from specific sections to its territorial conceptions and notions of simple
algebraic instances in this discussion section.
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10. Elementary Algebra on Vedic Mathematics 91
In the case of Paravartya Yojayet
• In terms of algebraic division, the Paravartya Yojayet formula is extremely
similar to the Remainder Theorem and the Horner process of synthetic division.
Horner's synthetic division method is only a minor part of the Paravartya
formula, which can be expanded to circumstances when the divisor is quadratic,
cubic, or any size polynomial.
• In the illustration part Paravartya formula of above sub-topic 2, the first
coefficient of g(x) was unity; there was no possibility of a fractional coefficient
in Q(x) being special cases. However, a lack of unity can lead to uncertainty,
redundancy, and other issues. As a result, the best option will be to divide the
divisor by its first coefficient right away and finish the calculation as in special
cases.
• The merger formula of Paravartya Yojayet can be extended to any finite
number of terms for solving equations.
• In the case of improper fractions, Paravartya Yojayet can be used by expressing
the numerator as the sum of polynomial and proper fractions.
• To find the partial fraction of the expression whose denominator is repeated i.e.
square, cube etc. there is slight variation in process is required by the formula
Paravartya Yojayet.
In the case of Sunyam Samyasamuccaye
ax + b ax + c
• It is clear that the expression = would be linear. But the
ax + b cx + d ax + c ax + b
expression = would be quadratic. It should be careful that N1 + N2
cx + d ax + b
= D1 + D2 and N1 – D1 = D2 – N2 in both cases.
2 3 1 6
• The expression of the form 2x + 3 + 3x + 2 =x + 1 + 6x + 7 when N1 × D2 = N2 ×
D1 & N3 × D4 = N4 × D3 (where N1, N2, N3, N4, D1, D2, D3, D4 have their usual
meanings) which can be changed into the (vi)th application.
In the case of Anurupye Sunyamanyat
• The formula is especially more useful for solving simultaneous equations
whose solution is complex being the large coefficients like 8906x + 45y = 73;
1953x + 31y = 63.
• The formula can be extended to any number of unknown quantities.
In the case of Antayoreva
• This formula is more valuable when the problem is unsolved by the formula
Sunyam Samyasamuccaye even the Samuccaye are equal in the case like (x+3)
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11. 92 K. K. Parajuli
x 2 + 3x + 2 x+3
(x+4) (x+5) = (x+1) (x+2) (x+9), which becomes 2
= then
x + 9 x + 20 x+9
−7
using antayoreva x = .
3
In the case of Lopanasthapanabhyam
• In most cases, eliminating two of the three variables is enough to factorize the
polynomials. There may arises some exceptional cases like x2 + xy – 2y2 +
2xz – 5yz – 3z2. By putting y = 0 yields (x – z) (x + 3z) and z = 0 yields (x – y)
(x +2y). Here is confusion to take right combination of factors. As a result, if
x is also removed, the factor will be (– y – z) (2y + 3z). Then there will be no
mistake about which factors to use. Hence, x2 + xy – 2y2 + 2xz - 5yz - 3z2 =
(x – y – z) (x +2y + 3z).
• Formulas from the Vedas Sankalana Vyavakalanabhyam and
Lopasthapanabhyam function together to find the HCF of an algebraic
expression using a Vedic approach, while the traditional method uses
factorization and continuous division.
Conclusions
The impression of Vedic methodologies that were more or less previously
assimilated or integrated in modern mathematical systems, such as Horner's
synthetic division process, Remainder theorem of polynomials, Crammer's rule,
cross multiplication method to solve simultaneous equations, factorizations of
polynomials, partial fractions of proper and improper rational functions. Except some
cases, conventional mathematics practitioners are utterly unaware of many of the
Vedic formulas mentioned in this paper. Even so, there are significant limitations to
Vedic formulas in specific cases involving elementary algebraic problems.
Under the presentation, demonstration, discussion, and outcomes of this paper,
the study concludes that Vedic Mathematics and its five specific Vedic formulas
are more valuable and practicable to those learners who are having difficulty with
elementary level algebra using traditional methods. Traditional students must use a
calculator to solve numerical and algebraic problems, whereas Vedic students may
solve similar problems mentally.
Suggestions
It is preferable to compare the methods to conventional approaches in order to
assess their value and effectiveness. Without really using the technique, the true beauty
and efficiency of these methods cannot be fully comprehended.
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12. Elementary Algebra on Vedic Mathematics 93
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Boyer, C. B. (1991). A History of Mathematics. New York: John Wiley & Sons, Inc.
Cajori, F. (1919). A History of Mathematics. New York: The Macmillan.
Dave, S., Fletcher, M., Glover, J., Prudente, V., Prodente, V., & Ramachandran, G.
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Mathematics Education Forum Chitwan, September 2021, Issue 6, Year 6

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