Question

Factor completely 81x2 − 4. (6 points) (2x − 9)(2x − 9) (2x − 9)(2x + 9) (9x − 2)(9x − 2) (9x − 2)(9x + 2)

Answer 1

(9x-2)(9x+2)
81x^2+18x-18x-4
81x^2-4

Answer 2

`(9x+2)(9x-2)`

Last option is correct.

Explanation:

The given expression is
`81x^2-4`

Write the expression in perfect squares

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

Apply the difference of squares formula:
`a^2-b^2=(a+b)(a-b)`

Here, a = 9x, b = 2

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

Therefore, the factored form is
`(9x+2)(9x-2)`

Last option is correct.