Factorize:$x^3 + 8y^3 + 6x^2y + 12xy^2$

Given:

$x^3 + 8y^3 + 6x^2y + 12xy^2$

To do:

We have to factorize the given expression.

Solution:

We know that,

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$

Therefore,

$x^3 + 8y^3 + 6x^2y + 12xy^2 = (x)^3 + (2y)^3 + 3 \times x^2 \times 2y + 3 \times x \times (2y)^2$

$= (x + 2y)^3$

$= (x + 2y) (x + 2y) (x + 2y)$

Hence, $x^3 + 8y^3 + 6x^2y + 12xy^2 = (x + 2y) (x + 2y) (x + 2y)$.

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Updated on: 10-Oct-2022

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