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. $\(\left\)(9-G\(\right\))\(\left\)(9+G\(\right\))$

Answer: (D)

Verified step by step guidance

1. Recall the Difference of Squares formula: \(a^2 - b^2 = (a - b)(a + b)\), which allows you to factor expressions that are the difference between two perfect squares.
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\( is a perfect square since \)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.
4. Apply the difference of squares formula by writing the factored form as \((a - b)(a + b)\).
5. Check your factored expression by expanding it back using the distributive property to ensure it matches the original expression.