Find the value of $ a^{3}+b^{3}+3 a b^{2}+3 a^{2} b $ if $ a=2, b=-3 $.
Given:
\( a=2, b=-3 \).
To do:
We have to find the value of \( a^{3}+b^{3}+3 a b^{2}+3 a^{2} b \).
Solution:
We know that,
$(a+b)^3=a^{3}+b^{3}+3 a b^{2}+3 a^{2} b$
Therefore,
$a^{3}+b^{3}+3 a b^{2}+3 a^{2} b=(a+b)^3$
$=(2+(-3))^3$
$=(2-3)^3$
$=(-1)^3$
$=-1$.
The value of $a^{3}+b^{3}+3 a b^{2}+3 a^{2} b$ is $-1$.
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