Question

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

Answer 1

$$4x^4+1$$

$$=4x^4+4x^2+1-4x^2$$

$$=[(2x^2{)}^2+2\times 2x^2\times 1+1]-4x^2$$

$$=(2x^2+1{)}^2-(2x{)}^2$$

$$=[(2x^2+1)-2x][(2x^2+1)+2x]$$

$$=(2x^2-2x+1)(2x^2+2x+1)$$