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

Given:

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

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,

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

$= (2x + y)^3$

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

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

Tutorialspoint

Updated on: 10-Oct-2022

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