Question

factorize:x^4-7x^2+1

Answer 1

In view of using the identity $a^2-b^2=(a+b)(a-b)$, split the middle term as $2x^2-9x^2$ :

$x^4\underbrace{-7x^2}+1$

$=x^4\underbrace{+2x^2-9x^2}+1$

$=(x^4+2x^2+1)-(9x^2)$

$=(x^2+1)^2-(3x)^2~~~\because~a^2+2ab+b^2=(a+b)^2$

$=(x^2+1+3x)(x^2+1-3x)$

$=(x^2+3x+1)(x^2-3x+1)$