Find the following product: (3 p^2+q^2 ) (2 p^2-3 q^2 )

Question

Find the following product:
$\left(3 p^2+q^2\right)\left(2 p^2-3 q^2\right)$

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Answer

$\left(3 p^2+q^2\right)\left(2 p^2-3 q^2\right)$
$=3 p^2\left(2 p^2-3 q^2\right)+q^2\left(2 p^2-3 q^2\right)$
$=\left(3 p^2 \times 2 p^2-3 p^2 \times 3 q^2\right)+\left(q^2 \times 2 p^2-q^2 \times 3 q^2\right)$
$=6 p^4-9 p^2 q^2+2 q^2 p^2-3 q^4$
$=6 p^4-7 p^2 q^2-3 q^4$

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