(Mathematic Form 3) Factorising Expressions

Factorising is the reverse process of expansion.

When you factorise an expression, you write it as a product of two or more common factors.

Tip: You may have to find the Highest Common Factor (HCF) for the terms first in order to arrive at an answer.

Eg:

Factorise each of the following:
i) 3p + 6
ii) 8a ² - 6ab
iii) ab + ac + bd + cd

Solution:

i) 3p + 6 ( 3 is the HCF)
= 3(p + 2)

ii) 8a ² - 6ab (2a is the HCF)
= 2a(4a - 3b)

iii) ab + ac + bd + cd
= a(b + c) + d(b + c)
= (b + c) (a + d)

Factorisation is also done by using the difference of two squares:

(a ² - b ²) = (a + b) (a - b)

or by your knowledge of perfect squares:

a ² + 2ab + b ² = (a + b) ²
a ² - 2ab + b ² = (a - b) ²

Eg:

Factorise 4p ² - 25q ²

Solution:

4p ² - 25q ²
= (2p + 5q) (2p - 5q)