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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Updated on: 10-Oct-2022

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