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SAI International School

CLASS – VIII
SUB: MATH

Ch -14: FACTORISATION
LESSON NOTES-6

SUBTOPIC:

 Factorisation using identity (x+a)(x+b), Fourth Identity

1. Factorisation using identity (x+a)(x+b)
(x+a) ×(x+b) is the fourth identity.

Let’s find that whether this identity is true or not,
First take the left hand side of the identity and do the multiplication.

LHS:- 㞘 ঑ 㞘 ′
= Ǥ 㞘 Ǥ′ 㞘 ঑Ǥ 㞘 ঑Ǥ′
(take the common factor from both the middle terms )
= 㞘 ঑ 㞘 ′࢈ 㞘 ঑′
= RHS
Example:-

Find the product of (z + 1)(z + 3) using the standard formula.

Solution:

We know, (x + a)(x + b) = + (a + b)x + ab.

Therefore, (z + 1)(z + 3) = + (1 + 3)z + 1 ∙ 3.

= + 4z + 3

Example 2:- (x + 2)(x + 5),

we obtain

(x + 2)(x + 5) = x(x + 5) + 2(x + 5)
= x + 5x + 2x + 10
2
2
= x + 7x + 10.

This expansion produces a simple quadratic. We would like to find a procedure that reverses

this process.

We notice that the coefficient x of is the sum of the two numbers 2 and 5 in the brackets and
that the constant term 10, is the product of 2 and 5. This suggests a method of factoring.

Example 3:-

Factor x + 7x + 12.
2