Factorise: $343 y^{3} - 125$

(7 y + 5) (49 y^{2} + 35 y + 25)

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(7 y - 5) (49 y^{2} - 35 y + 25)

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(7 y - 5) (49 y^{2} - 35 y - 25)

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(7 y - 5) (49 y^{2} + 35 y + 25)

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Solution

The correct option is D $(7 y - 5) (49 y^{2} + 35 y + 25)$
$343 y^{3} - 125 = (7 y)^{3} - 5^{3}$
We know that the difference of two cubes, $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
So, $(7 y)^{3} - 5^{3} = (7 y - 5) ((7 y)^{2} + 35 y + 5^{2})$
$(7 y)^{3} - 5^{3} = (7 y - 5) (49 y^{2} + 35 y + 25)$

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