Factories. (1 ) $x^{3} + 64 y^{3}$
(2) $24 a^{3} + 81 b^{3}$

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Solution

Using the identity $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

$(1) x^{3} + 64 y^{3}$

$= x^{3} + {(4 y)}^{3}$ where $a = x, b = 4 y$

$= (x + 4 y) (x^{2} - x \times 4 y + {(4 y)}^{2})$

$= (x + 4 y) (x^{2} - 4 x y + 16 y^{2})$

$(2) {24 a}^{3} + 81 b^{3}$

$= 3 ({(2 a)}^{3} + {(3 b)}^{3})$

$= 3 ({(2 a)}^{3} + {(3 b)}^{3})$

$= 3 (2 a + 3 b) (4 a^{2} - 6 a b + 9 b^{2})$

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