Question

Factorise each of the following rational expression
$\begin{array}{cc}& x^4+4\\ & x^4+4x^2+3\end{array}$

Answer 1

$\left(1\right)x^4+4⟹(x^2{)}^2+(2{)}^2$

$⟹(x^2+2{)}^2-4x^2$

$⟹(x^2+2{)}^2-(2x{)}^2$

$⟹(x^2+2-2x)(x^2+2+2x)$

$\left(2\right)x^4+4x^2+3$

$⟹x^4+x^2+3x^2+3$

$⟹x^4+4x^2+3$

$⟹x^4+x^2+3x^2+3$

$⟹x^2(x^2+1)+3(x^2+1)$

$⟹(x^2+1)(x^2+3)$