Question

Factor the expression completely.

18x2 - 32
O A. 2(3x + 2)(3x – 8)
B. 2(9x2 - 16)
O C. 2(3x - 4)(3x - 4)
O D. 2(3x + 4)(3x - 4)

Answer 1

`\fbox{\begin{minipage}{13em}Option D: 2(3x + 4)(3x - 4)\end{minipage}}`

Explanation:

`A = 18x^(2) - 32\\`

Find the sharing components:

<=>
`A=2*9*x^(2) - 2*16`

Apply the inverse of associative property:

<=>
`A = 2(9x^(2) - 16)`

Identify two square components inside the parenthesis:

<=>
`A = 2((3x)^(2) - 4^(2) )`

Factorize:

<=>
`A = 2(3x + 4)(3x - 4)`

=> Option D is correct

Hope this helps!

:)