Factorize each of the following expressions:$125 + 8x^3 - 27y^3 + 90xy$

Given:

$125 + 8x^3 - 27y^3 + 90xy$

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,

$125 + 8x^3 - 27y^3 + 90xy = (5)^3 + (2x)^3 + (-3y)^3 - [3 \times 5 \times 2x \times (-3y)]$

$= (5 + 2x - 3y) [(5)^2 + (2x)^2 + (-3y)^2 - 5 \times 2x - 2x \times (-3y) - (-3y) \times 5]$

$= (5 + 2x - 3y) (25 + 4x^2 + 9y^2 - 10x + 6xy + 15y)$

Hence, $125 + 8x^3 - 27y^3 + 90xy = (5 + 2x - 3y) (25 + 4x^2 + 9y^2 - 10x + 6xy + 15y)$.

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Updated on: 10-Oct-2022

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