Factors of $x^{3} - 27 y^{3} + 125 + 45 x y$ are ?

(x^{2} + 9 y^{2} + 25 + 3 x y + 5 y - 5 x)

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(x - 3 y + 5)

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1

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None of these

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Solution

The correct options are
A $(x^{2} + 9 y^{2} + 25 + 3 x y + 5 y - 5 x)$
B $(x - 3 y + 5)$
C $1$
$x^{3} - 27 y^{3} + 125 + 45 x y$
Using, $a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - a c - b c)$
$= x^{3} - (3 y)^{3} + 5^{3} - 3 (x) (- 3 y) (5)$
$= (x - 3 y + 5) (x^{2} + (3 y)^{2} + 5^{2} - x . (- 3 y) - x (5) - (- y) 5)$
$= (x - 3 y + 5) (x^{2} + 9 y^{2} + 25 + 3 x y + 5 y - 5 x)$

Suggest Corrections

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Factors of

$- x^{3} - 125$

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