Question

Factorise the following by taking out the common factors:
36(x + y)³ - 54(x + y)²

Answer 1

36(x + y)³ - 54(x + y)² 
Here, the common factor is 18(x + y)².
Dividing throughout by 18(x + y)², we get

${\displaystyle \frac{36{(x+y)}^3}{18{(x+y)}^2}-\frac{54{(x+y)}^2}{18{(x+y)}^2}}$
= 2(x + y) - 3
∴ 36(x + y)³ - 54(x + y)²
= 18(x + y)²[2(x + y) - 3].