Find the following products:
$(3x + 2y) (9x^2 - 6xy + 4y^2)$

Given: 

$(3x + 2y) (9x^2 - 6xy + 4y^2)$

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,

$(3 x+2 y)(9 x^{2}-6 x y+4 y^{2})=(3 x+2 y)[(3 x)^{2}-3 x \times 2 y+(2 y)^{2}]$

$=(3 x)^{3}+(2 y)^{3}$

$=27 x^{3}+8 y^{3}$

 Hence, $(3 x+2 y)(9 x^{2}-6 x y+4 y^{2})=27 x^{3}+8 y^{3}$.

Tutorialspoint

Updated on: 10-Oct-2022

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