Question

Factor completely 81x4 − 16.

(3x − 2)(3x − 2)(9x2 + 4)
(3x − 2)(3x + 2)(9x2 − 4)
(3x − 2)(3x + 2)(9x2 + 4)
(3x + 2)(3x + 2)(9x2 + 4)

Answer 1

`(9x^(2) +4)(3x+2)(3x-2)`

Option C

Explanation:

Given,

`81x^(4) -16`

To find the factors.

Formula:

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

Now,

`81x^(4) -16`

=
`(9x^(2) )^(2)-4^(2)`

=
`(9x^(2)+4)(9x^(2)-4)`

=
`(9x^(2)+4) ((3x)^(2) -2^(2) )`

=
`(9x^(2) +4)(3x+2)(3x-2)`