Simplify the following:$(4a-3)^3 - (4a+3)^3$

Given :

The given expression is $(4a-3)^3 - (4a+3)^3$.

To do :

We have to simplify the given expression.

Solution :

We know that,

$(a-b)^3-(a+b)^3 = a^3-b^3-3a^2b+3ab^2-(a^3+b^3+3a^2b+3ab^2)$

                         $= a^3-b^3-3a^2b+3ab^2- a^3-b^3-3a^2b-3ab^2$

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

                         $=-(2b^3+6a^2b)$

Therefore,

 $(4a-3)^3 - (4a+3)^3 = -[2(3)^3 +6(4a)^2(3)]$

                                 $= -[2(27)+18(16)a^2]$

                                 $= -(54+288a^2)$

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Updated on: 10-Oct-2022

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