Question

Factorize each of the following algebraic expression:
4x⁴ + y⁴

Answer 1

$$\begin{gathered} 4{\mathrm{x}}^4+{\mathrm{y}}^4 \\ =4{\mathrm{x}}^4+4{\mathrm{x}}^2{\mathrm{y}}^2+{\mathrm{y}}^4-4{\mathrm{x}}^2{\mathrm{y}}^2 \\ =\left[\right(2{\mathrm{x}}^2{)}^2+2\times 2{\mathrm{x}}^2\times \mathrm{y}+\left({\mathrm{y}}^2{)}^2\right]-(2\mathrm{xy}{)}^2 \\ =(2{\mathrm{x}}^2+{\mathrm{y}}^2{)}^2-(2\mathrm{xy}{)}^2 \\ =[(2{\mathrm{x}}^2+{\mathrm{y}}^2)-2\mathrm{xy}\left]\right[(2{\mathrm{x}}^2+{\mathrm{y}}^2)+2\mathrm{xy}] \\ =(2{\mathrm{x}}^2-2\mathrm{xy}+{\mathrm{y}}^2\left)\right(2{\mathrm{x}}^2+2\mathrm{xy}+{\mathrm{y}}^2) \end{gathered}$$