FACTORISATIONS

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) 8a2 - 6ab
iii) ab + ac + bd + cd

Solution:

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

ii) 8a2 - 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:

(a2 - b2) = (a + b) (a - b)

or by your knowledge of perfect squares:

a2 + 2ab + b2 = (a + b)2
a2 - 2ab + b2 = (a - b)2

Eg:

Factorise 4p2 - 25q2

Solution:

4p2 - 25q2
= (2p + 5q) (2p - 5q)

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Factorise the following:

a. 10a + 15 = 5(2a + 3)

b. 12ab - 18b2 = 6b(2a - 3b)

c. 4mn + 12mn2 = 4mn(1 + 3n)

d. 9x2 - 64y2 = (3x + 8y) (3x - 8y)

e. 4p2 - 100q2 = 4(p + 5q) (p - 5q)

f. 12a2 - 48b2 = 12(a + 2b) (a - 2b)

g. x2 + 6xy + 9y2 = (x + 3y)2

h. 3p2 + 6pq + 3q2 = 3(p + q)2

i. a2 + ab + 3a + 3b = (a + 3) (a + b)

j. mk - m2 + 4k - 4m = (m + 4) (k - m)

k. (a - 7)2 - 100 = (a + 3) (a - 17)