Write the following difference of squares as a product of two binomials.
$81-G^2$

• A. $(81-G)(81+G)$
• B. $(9-G^2)(9+G^2)$
• C. $(9-G)(9-G)$
• D. $(9-G)(9+G)$

Answer: (D)

Verified step by step guidance

1. Recall the Difference of Squares formula: \(a^2 - b^2 = (a - b)(a + b)\). This formula helps factor expressions where you have one perfect square minus another perfect square.
2. Identify the two perfect squares in the given expression. For example, if the expression is \(x^2 - 9\), recognize that \(x^2\) is a perfect square and \$9\( is also a perfect square since \)9 = 3^2$.
3. Rewrite the expression in the form \(a^2 - b^2\), where \(a\) and \(b\) are the square roots of the two perfect squares identified. Using the example, rewrite \(x^2 - 9\) as \((x)^2 - (3)^2\).
4. Apply the difference of squares formula by writing the factored form as \((a - b)(a + b)\). For the example, this becomes \((x - 3)(x + 3)\).
5. Check your factored expression by expanding it back using the distributive property (FOIL) to ensure it equals the original expression.