Question

Simplify the following products:

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

Answer 1

Given, $(2x^4-4x^2+1)(2x^4-4x^2-1)$
$=\left(\right(2x^4-4x^2)+1)\left(\right(2x^4-4x^2)-1)$
using identity $(a-b)(a+b)=a^2-b^2$
$=\left(\right(2x^4-4x^2{)}^2-1^2)$
using identity $(a-b{)}^2=a^2-2ab+b^2$
$=\left(\right(2x^4{)}^2-2\times 2x^4\times 4x^2+(4x^2{)}^2-1^2)$
$=4x^8-16x^6+16x^4-1$

Hence, $(2x^4-4x^2+1)(2x^4-4x^2-1)=4x^8-16x^6+16x^4-1.$