Simplify each of the following:$ (2 x-5 y)^{3}-(2 x+5 y)^{3} $

Given:

\( (2 x-5 y)^{3}-(2 x+5 y)^{3} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

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

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

Therefore,

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

$=[8 x^{3}-125 y^{3}-60 x^{2} y+150 x y^{2}]-[8 x^{3}+125 y^{3}+60 x^{2} y+150 x y^{2}]$

$=8 x^{3}-125 y^{3}-60 x^{2} y+150 x y^{2}-8 x^{3}-125 y^{3}-60 x^{2} y-150 x y^{2}$

$=-250 y^{2}-120 x^{2} y$

Hence, $(2 x-5 y)^{3}-(2 x+5 y)^{3}=-250 y^{2}-120 x^{2} y$.

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Updated on: 10-Oct-2022

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