Factorise the following by taking out the common factors:
j) $36 (x + y)^{3} - 54 (x + y)^{2}$

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Solution

Given: $36 (x + y)^{3} - 54 (x + y)^{2}$

The common factor is $18 (x + y)^{2}$ .

Dividing by $18 (x + y)^{2}$ in the above expression, we get ,

$\frac{36 (x + y)^{3}}{18 (x + y)^{2}} - \frac{54 (x + y)^{2}}{18 (x + y)^{2}}$

$= 2 (x + y) - 3$

$∴ 36 (x + y)^{3} - 54 (x + y)^{2} = 18 (x + y)^{2} (2 (x + y) - 3)$

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