Factorize: $8 x^{3} + 125 y^{3}$

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Solution

Given: $8 x^{3} + 125 y^{3}$
$= (2 x)^{3} + (5 y)^{3}$
$= (2 x + 5 y) [(2 x)^{2} - (2 x) (5 y) + (5 y)^{2}]$ [ $∵ a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})]$
$= (2 x + 5 y) (4 x^{2} - 10 x y + 25 y^{2})$

Hence, factorisation of $8 x^{3} + 125 y^{3}$ is $(2 x + 5 y) (4 x^{2} - 10 x y + 25 y^{2})$ .

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