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SAI International School
CLASS – VIII,
SUB: MATH

LESSON NOTES-4
Ch-14: FACTORISATION

SUBTOPIC:
 What are identities?
 Factorisation using identities
1) What are identities?
An identity is an equality that holds true regardless of the values chosen for its
variables. They are used in simplifying or rearranging algebra expressions. By
definition, the two sides of an identity are interchangeable, so we can replace one with
the other at any time.

The algebraic identities are verified using the substitution method. In this method,
substitute the values for the variables and perform the arithmetic operation. Another
method to verify the algebraic identity is the activity method. In this method, you should
need a prerequisite knowledge of Geometry and some materials needed to prove the
identity.
We are going to factorised the first identities

Again

ܽ ܽ

ܽ ܽ ܽ
ܽ ܽ ܽ
ܽ ܽ
ܽ (Identity 1)
Similarly we can factorise identity 2

ܽ ܽ

ܽ ܽ ܽ
ܽ ܽ ܽ
ܽ ܽ
ܽ (Identity 2)
2) Factorisation using identities

In the 1st identity, a + 2ab + b = (a + b) ,
2
2
2
1st and the last term should be perfect square and the middle term is two times the
square root of 1st and the last term and the sign of the middle term is positive.