Algebra Formula for Class 10

A combination of constants and variables connected by the signs of the fundamental operation of addition, subtraction, multiplication, and division is called an algebraic expression. Various parts of an algebraic expression that are separated by the signs of + or - are called the terms of the expression. Here is the list of Algebra Formula for class 10 that will help students to guide them in their study of algebra.

An algebraic expression is defined as a sum, difference, product or quotient of constants and variables. 

Consider,

 12x + 50

Here this expression is called an algebraic expression where x varies in values so it is a variable and 50 is constant. 12x and 50 are the terms and they are separated by the sign +. We can write anything a, b, c ….z in place of variables.


Algebra Class 10

Algebra is one of the branches of Mathematics which deals with variables and numbers.

Algebra for class 10 consist of different methods of solving a pair of linear equations:

1.Elimination Method

2. Substitution Method

3.Cross Multiplication Method


Algebraic Identities Class 10

There are some Algebraic identities that involve products of specific kinds of algebraic expressions. Here are some of the Algebraic Identities used in class 10. 

  • (l+m)2 = l2 + m2 + 2lm

  • (l-m)2 = l2 + m2 – 2lm

  • (l+m) (l-m) = l2 – m2

  • (x + l)(x + m) = x2 + (l + m)x + lm

  • (x + l)(x – m) = x2 + (l – m)x – lm

  • (x – l)(x + m)  = x2 + (m – l)x – lm

  • (x – l)(x – m)  = x2 – (l + m)x + lm

  • (l + m)3  = l3 + m3 + 3lm(l + m)

  • (l – m)3  = l3 – m3 – 3lm(l – m)

  • (x + y + z)2  = x2 + y2 + z2 + 2xy + 2yz + 2xz

  • (x + y – z)2  = x2 + y2 + z2 + 2xy – 2yz – 2xz

  • (x – y + z)2  = x2 + y2 + z2 – 2xy – 2yz + 2xz

  • (x – y – z)2  = x2 + y2 + z2 – 2xy + 2yz – 2xz

  • x3 + y3 + z3 – 3xyz  = (x + y + z)(x2 + y2 + z2 – xy – yz -xz)

  • x2 + y2  = ½ [(x + y)2 + (x – y)2]

  • (x + a) (x + b) (x + c)  = x3 + (a + b +c)x2 + (ab + bc + ca)x + abc

  • x3 + y3 =  (x + y) (x2 – xy + y2)

  • x3 – y3 = (x – y) (x2 + xy + y2)

  • x2 + y2 + z2 -xy – yz – zx  = 1/2 [(x-y)2 + (y-z)2 + (z-x)2]


 Formulas for Powers

  • pm x pn = pm+n

  • {pm}⁄{pn} = pm-n

  • (pm)n = pmn

  • p-m = 1/pm

  • p1 = p

  • P0 = 1


Polynomial Formulas

  • axn+bxn−1+…..+rx+s=0axn+bxn−1+…..+rx+s=0

  • an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1) where  n is a natural number,

  •  (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1) where n is even number

  • (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1) where n is odd number

  • (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….)


10th Standard Algebra

10th standard Algebra becomes easy to solve once you get acquainted with these formulas. Grasping these formulas helps you to solve the algebraic equation more effectively.


10th Algebra Formulas

10th Algebra Formulas are of foremost importance at every level of competitive exams. You should memorize these formulas to crack all the Math competitive exams.

The main objective of solving the algebraic equation is to find the unknown variables in the expression.


Fun Facts:

  •  It was Babylonians who came up with Algebra in 1900 BC.

  • The use of signs addition(+) and subtraction(-) prove to be beneficial in performing algebraic equations. Before that, people use written words to express the functions of addition and subtraction which was a time-consuming process.


Solved Examples:

Example 1 : If a = 3, b =2 , find the value of 4a + 5b -7

Solution:

4a + 5b-7

Substituting the values of a and b in the given algebraic expression, we get

4a + 5b - 7

= 4 x 3 + 5 x 2 - 7

= 12 + 10 - 7

= 22 - 7

=15


Example 2: Expand (p - 4) (2p + 9)

Solution: = p(2p + 9) - 4(2p +9)

    = 2p2 + 9p - 8p -36

    = 2p2 + p -36


Quiz:

1.Expand each of the following.

  •  (c + 8)(c - 9)

  • (d - 2)(d - 6)

2.If p= 5 and q = 1 find the value of 2pq + p2 - q2

FAQ (Frequently Asked Questions)

1. What is Algebraic Equation?

Solution: An equation which is the combination of constants and variables connected by the signs of +,-, / or x is equal to another equation is called an algebraic equation.

A mathematical statement is said to be an algebraic equation if the left-hand side equation is equal to the right-hand side equation. That means values to both sides of equal to sign are equal.

Consider an equation 5 + 2 = 3 + 4 here, you can see both sides have the value 6. Such expressions are called algebraic equations.

2. What is the Difference Between the Algebraic Equation and Algebraic Expression?

Solution: Students are often confused about the term Algebraic Equation and Algebraic expression. Let us make it more clear.

  • An algebraic expression is a single equation with no equality sign, whereas the Algebraic equation is a set of two equations that have equality sign between them.

  • An algebraic expression is of form 2x + 3y - x + y. 

  • An Algebraic equation is of the form 5x + 2 = 0.

  • An Algebraic expression can be expanded or simply whereas, an algebraic equation has to be solved, it has a certain value.

  • The algebraic expression will be true for any value of x, while the algebraic equation will be true only for some values of x.