Multiply the following : (3 2 p^2+2 3 q^2 ), (2 p^2-3 q^2 ) - Vidyadip

Question

Multiply the following :
$\left(\frac{3}{2} p^2+\frac{2}{3} q^2\right),\left(2 p^2-3 q^2\right)$

✓

Answer

We have, $\left(\frac{3}{2} p^2+\frac{2}{3} q^2\right)$ and $\left(2 p^2-3 q^2\right)$
$\therefore\left(\frac{3}{2} p^2+\frac{2}{3} q^2\right)\left(2 p^2-3 q^2\right)= \frac{3}{2} p^2\left(2 p^2-3 q^2\right) +\frac{2}{3} q^2\left(2 p^2-3 q^2\right)$
$=\frac{3}{2} p^2 \times 2 p^2-\frac{9}{2} p^2 q^2+\frac{4}{3} q^2 p^2-2 q^4$
$=3 p^4+\left(\frac{4}{3}-\frac{9}{2}\right) p^2 q^2-2 q^4$
$=3 p^4+\left(\frac{8-27}{6}\right) p^2 q^2-2 q^4$
$=3 p^4-\frac{19}{6} p^2 q^2-2 q^4$

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