Simplify each of the following products:$ (x^{2}+x-2)(x^{2}-x+2) $

Given:

\( (x^{2}+x-2)(x^{2}-x+2) \)

To do:

We have to simplify the given product.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$(x^{2}+x-2)(x^{2}-x+2)=[x^{2}+(x-2)][x^{2}-(x-2)]$

$=(x^{2})^{2}-(x-2)^{2}$

$=x^{4}-[(x)^{2}-2 \times x \times 2+(2)^{2}]$

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

$=x^{4}-x^{2}+4 x-4$

Hence, $(x^{2}+x-2)(x^{2}-x+2)=x^{4}-x^{2}+4 x-4$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

19 Views

Kickstart Your Career

Get certified by completing the course

Get Started