Question

X^4-14x^2+1 factorize it please just now.

Answer 1

Just arrange all the terms and factorize using the formula a^2+b^

Answer 2

The factorisation of $x^{4} -14x^{2} +1$ is $(x^{2}+1+4x)(x^{2}+1-4x)$.

Step-by-step explanation:

We have,

$x^{4} -14x^{2} +1$

To find, the factorisation of $x^{4} -14x^{2} +1=?$

∴ $(x^{4} +1)-14x^{2}$

=$((x^{2})^{2} +1^{2} )-14x^{2}$

$=(x^{2}+1)^{2} -2x^{2}-14x^{2}$

[ ∵ $a^{2} +b^{2} =(a+b)^{2} -2ab$]

$=(x^{2}+1)^{2} -16x^{2}$

$=(x^{2}+1)^{2} -(4x)x^{2}$

$=(x^{2}+1+4x)(x^{2}+1-4x)$

[ ∵ $a^{2} -b^{2}=(a+b)(a-b)$]

Hence, the factorisation of $x^{4} -14x^{2} +1$ is $(x^{2}+1+4x)(x^{2}+1-4x)$.