Find the value of $x^3-8y^3-36xy$ when $x = 2y + 6$.

Given :

The given expression is $x^3-8y^3-36xy$

To do :

We have to find the value of $x^3-8y^3-36xy$ at $x=2y+6$.

Solution :

$x = 2y+6$

We know that,

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

$x = 2y+6$

$x-2y = 6$

Cubing on both sides, we get,

$(x-2y)^3= (6)^3$

$x^3-(2y)^3-3(x)(2y)(x-2y) = 216$

$x^3-8y^3-6xy(6) = 216$

$x^3-8y^3-36xy = 216$.

The value of $x^3-8y^3-36xy$ is $216$.

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Updated on: 10-Oct-2022

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