Question

Find the products
(1/4x2+3y2) (4x2-1/3y2)

Answer 1

$$\begin{gathered} \left(\frac{{\mathrm{x}}^2}{4}+3{\mathrm{y}}^2\right)\left(4{\mathrm{x}}^2-\frac{{\mathrm{y}}^2}{3}\right) \\ =\frac{{\mathrm{x}}^2}{4}\left(4{\mathrm{x}}^2-\frac{{\mathrm{y}}^2}{3}\right)+3{\mathrm{y}}^2\left(4{\mathrm{x}}^2-\frac{{\mathrm{y}}^2}{3}\right) \\ =\frac{{\mathrm{x}}^2}{4}\times 4{\mathrm{x}}^2-\frac{{\mathrm{x}}^2}{4}\times \frac{{\mathrm{y}}^2}{3}+3{\mathrm{y}}^2\times 4{\mathrm{x}}^2-3{\mathrm{y}}^2\times \frac{{\mathrm{y}}^2}{3} \\ ={\mathrm{x}}^4-\frac{{\mathrm{x}}^2{\mathrm{y}}^2}{12}+12{\mathrm{x}}^2{\mathrm{y}}^2-{\mathrm{y}}^4 \end{gathered}$$