Question

Factorise each of the following:

$27–125a^3–135a+225a^2$ [3 MARKS]

Answer 1

Formula: 1 Mark
Application: 2 Marks

${(x-y)}^3=x^3-y^3-3xy(x-y)$

$=x^3-3x^{2}y+3x{y}^2-y^3$

$27–125a^3–135a+225a^2$
[Comparing with above identity]

$=3^3–{\left(5a\right)}^3–3{\left(3\right)}^2\left(5a\right)+3\left(3\right){\left(5a\right)}^2$

$={(3-5a)}^3$