Question

Factorize each of the following algebraic expression:
4x⁴ + 1

Answer 1

$$\begin{gathered} 4{\mathrm{x}}^4+1 \\ =4{\mathrm{x}}^4+4{\mathrm{x}}^2+1-4{\mathrm{x}}^2 \\ =\left[\right(2{\mathrm{x}}^2{)}^2+2\times 2{\mathrm{x}}^2\times 1+1]-4{\mathrm{x}}^2 \\ =(2{\mathrm{x}}^2+1{)}^2-(2\mathrm{x}{)}^2 \\ =[(2{\mathrm{x}}^2+1)-2\mathrm{x}\left]\right[(2{\mathrm{x}}^2+1)+2\mathrm{x}] \\ =(2{\mathrm{x}}^2-2\mathrm{x}+1\left)\right(2{\mathrm{x}}^2+2\mathrm{x}+1) \end{gathered}$$