81x^4-1 factor with steps

Question

asked Apr 8, 2022 179k views

1 Answer

SmartyP · Answer 1 · 2022-04-14T17:02:33+0000

Given:

The expression is

81x^4-1

To find:

The factorized form of given expression.

Solution:

We have,

81x^4-1

It can be rewritten as

=3^4x^4-1^2

=(3x)^4-1^2
$[\because a^xb^x=(ab)^x]$

=((3x)^2-1)((3x)^2+1)
$[\because a^2-b^2=(a-b)(a+b)]$

=(3x+1)(3x-1)(3x+1)(3x-1)
$[\because a^2-b^2=(a-b)(a+b)]$

This is the complete factorized form. It can also written as

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

Therefore, the complete factorized form is
.