Question

Find the product:

(3p² + q²)(2p² − 3q²)

Answer 1

$$\begin{gathered} (3{\mathrm{p}}^2+{\mathrm{q}}^2(2{\mathrm{p}}^2-3{\mathrm{q}}^2) \\ =3{\mathrm{p}}^2\times (2{\mathrm{p}}^2-3{\mathrm{q}}^2)+{\mathrm{q}}^2\times (2{\mathrm{p}}^2-3{\mathrm{q}}^2) \\ =(3{\mathrm{p}}^2\times 2{\mathrm{p}}^2-3{\mathrm{p}}^2\times 3{\mathrm{q}}^2)+({\mathrm{q}}^2\times 2{\mathrm{p}}^2-{\mathrm{q}}^2\times 3{\mathrm{q}}^2) \\ =6{\mathrm{p}}^4-9{\mathrm{p}}^2{\mathrm{q}}^2+2{\mathrm{q}}^2{\mathrm{p}}^2-3{\mathrm{q}}^4 \\ =6{\mathrm{p}}^4-7{\mathrm{p}}^2{\mathrm{q}}^2-3{\mathrm{q}}^4 \end{gathered}$$