Question

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

Answer 1

\[4 x^4 + 1\]

\[ = 4 x^4 + 4 x^2 + 1 - 4 x^2 \]

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

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

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

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