Question

Which expression is equivalent to 64 − 9x2?

(32)2 − (3x)2
(32)2 + (−3x)2
(8)2 − (3x)2
(8)2 + (−3x)2

Answer 1

ANSWER


`64 - 9 {x}^(2) = {8}^(2) -( {3x)}^(2)`

EXPLANATION
The given expression is


`64 - 9 {x}^(2)`

Rewrite to get:


`{8}^(2) - {3}^(2) {x}^(2)`

Recall that


`{a}^(n) {b}^(n) = {(ab)}^(n)`
We apply this property of exponents to the second term.

This gives us


`64 - 9 {x}^(2) = {8}^(2) -( {3x)}^(2)`

The third choice is correct.

Answer 2

Answer: Third option.

Explanation:

By definition, the number 64 and the number 9 are perfect squares.

A perfect square it that number obtained by squaring a whole number.

In this case, 64 is obtained by squaring the number 8 and the number 9 is obtained by the squaring the number 3. Then:

`8^2=64\\3^2=9`

Therefore, you can rewrite the expression
`64-9x^2` as following:

`(8)^2-(3x)^2`

This matches with the third option.