What is the factor of $y^{3} - 125$ ?

(y + 5) (y^{2} + 5 y + 25)

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(y - 5) (y^{2} + 5 y + 25)

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(y - 5) (y^{2} - 5 y + 25)

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(y - 5) (y^{2} - 5 y - 25)

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Solution

The correct option is B $(y - 5) (y^{2} + 5 y + 25)$
$y^{3} - 125 = y^{3} - 5^{3}$
We know that the difference of two cubes, $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
So, $y^{3} - 5^{3} = (y - 5) (y^{2} + 5 y + 5^{2})$
$y^{3} - 5^{3} = (y - 5) (y^{2} + 5 y + 25)$

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