Factorise each of the following:

$27 y^{3} + 125 z^{3}$ [ 3 MARKS]

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Solution

Formula: 1 Mark
Application: 2 Marks

$27 y^{3} + 125 z^{3}$

$= {(3 y)}^{3} + {(5 z)}^{3}$

Using the identity
$x^{3} + y^{3} = (x + y) (x^{2} + y^{2} - x y)$
$= (3 y + 5 z) ({(3 y)}^{2} + {(5 z)}^{2} - (3 y) (5 z))$

$= (3 y + 5 z) ({9 y}^{2} + {25 z}^{2} - 15 y z)$

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