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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,
$(4a-3)^3 - (4a+3)^3 = -[2(3)^3 +6(4a)^2(3)]$
$= -[2(27)+18(16)a^2]$
$= -(54+288a^2)$
Therefore, the value of $(4a-3)^3 - (4a+3)^3$ is $-54-288a^2$.
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