Question

Which expression is equivalent to 64 − 9x2?

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.

Step-by-step 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.