Question

Factorise the following: $4x^4-5x^2+1$

Answer 1

Given: $4x^4-5x^2+1$

$=4y^2-5y+1$, (let $x^2=y$)

$=4y^2-4y-y+1$, (split the middle term)

$=(4y^2-4y)+(-y+1)$, (group pair of terms)

$=4y(y-1)-1(y-1)$, (factor each binomials)

$=(y-1)(4y-1)$, (factor out common factor $(y-1)$)

$=(x^2-1)(4x^2-1)$, (substitute back $y=x^2$)