Question

which expression is equivalent to (64 - 9x^2)?

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

((32)^2 - (3x)^2)

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

((32)^2 + (-3x)^2)

Explanation:

Identify the terms of the expression

We are given the algebraic expression:

$$64 - 9x^2$$

This expression consists of two terms separated by a subtraction sign.

Rewrite the first term as a perfect square

Using the Perfect Square Monomials knowledge point, we find a number that, when squared, equals \(64\).

$$64 = 8^2$$

Rewrite the second term as a perfect square

Using the Exponent Rules and Perfect Square Monomials knowledge points:

$$
LATEXBLOCK0
$$

Substitute the perfect squares back into the expression

Using the Exponent Rules knowledge point

$$64 - 9x^2 = (8)^2 - (3x)^2$$

Compare with the given options

We match our rewritten expression \((8)^2 - (3x)^2\) with the third option.

Answer:

• (A) \((8)^2 + (-3x)^2\)
• (B) \((32)^2 - (3x)^2\)
• (C) \((8)^2 - (3x)^2\) (Correct answer)
• (D) \((32)^2 + (-3x)^2\)