Factorize :
$x^{3} + 6 x^{2} y + 12 x y^{2} + 9 y^{3}$

(x - 3 y) (x^{2} + 3 y^{2} + 3 x)

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(x + 3 y) (x^{2} + 3 y^{2} + 3 x y)

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(x - y) (x^{2} + y^{2} + 3 y)

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(x + 4 y) (x^{2} + y^{2} + x y)

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Solution

The correct option is B $(x + 3 y) (x^{2} + 3 y^{2} + 3 x y)$
$x^{3} + 6 x^{2} y + 12 x y^{2} + 9 y^{3}$
$= x^{3} + 3 x^{2} y + 3 x y^{2} + 3 x^{2} y + 9 x y^{2} + 9 y^{3}$
$= x (x^{2} + 3 x y + 3 y^{2}) + 3 y (x^{2} + 3 x y + 3 y^{2})$
$= (x + 3 y) (x^{2} + 3 y^{2} + 3 x y)$

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Similar questions

5 x^{2} y - 5 x^{2} + 3 y x^{2} - 3 y^{2} + x^{2} - y^{2} + 8 x y^{2} - 3 y^{2}

5 x^{2} - 5 x^{2} + 3 y x^{2} - 3 y^{2} + x^{2} - y^{2} + 8 x y^{2} - 3 y^{2}

Question 1 (v)

Simplify combining like terms:

$5 x^{2} y - 5 x^{2} + 3 y x^{2} - 3 y^{2} + x^{2} - y^{2} + 8 x y^{2} - 3 y^{2}$

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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