Factorise x^4-256. - Vidyadip

Question

Factorise $x^4-256$.

✓

Answer

We have, $x^4-256$
$
\begin{array}{lr}
=\left(x^2 \times x^2\right)-(16 \times 16)=\left[\left(x^2\right)^2-(16)^2\right] \\
=\left(x^2+16\right)\left(x^2-16\right) & \text { [using Identity III] } \\
=\left(x^2+16\right)\left(x^2-4 \times 4\right) & \\
=\left(x^2+16\right)\left[(x)^2-(4)^2\right] & \\
=\left(x^2+16\right)(x+4)(x-4) & \text { [using Identity III] }
\end{array}
$

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