Factorize each of the following expressions:$8x^3 - 125y^3 + 180xy + 216$

Given:

$8x^3 - 125y^3 + 180xy + 216$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$

Therefore,

$8x^3 - 125y^3 + 180xy + 216 = (2x)^3 + (-5y)^3 + (6)^3 - 3 \times 2x \times (-5y) \times 6$

$= (2x - 5y + 6) [(2x)^2 + (-5y)^2 + (6)^2 - 2x \times (-5y) - (-5y) \times 6 - 6 \times 2x]$

$= (2x -5y + 6) (4x^2 + 25y^2 + 36 + 10xy + 30y - 12x)$

Hence, $8x^3 - 125y^3 + 180xy + 216 = (2x -5y + 6) (4x^2 + 25y^2 + 36 + 10xy + 30y - 12x)$.

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Updated on: 10-Oct-2022

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