Find the following products:
$(4x - 5y) (16x^2 + 20xy + 25y^2)$

Given: 

$(4x - 5y) (16x^2 + 20xy + 25y^2)$

To do: 

We have to find the given product.

Solution: 

We know that,

$a^{3}+b^{3}=(a+b)(a^{2}-a b+b^{2})$

$a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})$

Therefore,

$(4 x-5 y)(16 x^{2}+20 x y+25 y^{2})=(4 x-5 y)[(4 x)^{2}+4 x \times 5 y+(5 y)^{2}]$

$=(4 x)^{3}-(5 y)^{3}$

$=64 x^{3}-125 y^{3}$

 Hence, $(4 x-5 y)(16 x^{2}+20 x y+25 y^{2})=64 x^{3}-125 y^{3}$.

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Simply Easy Learning

Updated on: 10-Oct-2022

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