Question

Find the product:

(2x² − 5y²)(x² + 3y²)

Answer 1

$$\begin{gathered} (2{\mathrm{x}}^2-5{\mathrm{y}}^2)({\mathrm{x}}^2+3{\mathrm{y}}^2) \\ =2{\mathrm{x}}^2\times ({\mathrm{x}}^2+3{\mathrm{y}}^2)-5{\mathrm{y}}^2\times ({\mathrm{x}}^2+3{\mathrm{y}}^2) \\ =(2{\mathrm{x}}^2\times {\mathrm{x}}^2+2{\mathrm{x}}^2\times 3{\mathrm{y}}^2)-(5{\mathrm{y}}^2\times {\mathrm{x}}^2+5{\mathrm{y}}^2\times 3{\mathrm{y}}^2) \\ =2{\mathrm{x}}^4+6{\mathrm{x}}^2{\mathrm{y}}^2-5{\mathrm{y}}^2{\mathrm{x}}^2-15{\mathrm{y}}^4 \\ =2{\mathrm{x}}^4+{\mathrm{x}}^2{\mathrm{y}}^2-15{\mathrm{y}}^4 \end{gathered}$$