Factorize:$8x^3 + 27y^3 + 36x^2y + 54xy^2$

Given:

$8x^3 + 27y^3 + 36x^2y + 54xy^2$

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,

$8x^3 + 27y^3 + 16x^2y + 54xy^2 = (2x)^3 + (3y)^3 + 3 \times (2x)^2 \times 3y + 3 \times 2x \times (3y)^2$

$= (2x + 3y)^3$

$= (2x + 3y) (2x + 3y) (2x + 3y)$

Hence, $8x^3 + 27y^3 + 16x^2y + 54xy^2 = (2x + 3y) (2x + 3y) (2x + 3y)$.

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Updated on: 10-Oct-2022

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