Write the following difference of squares as a product of two binomials.
$k^2-49$

• A. $\(\left\)(k-7\(\right\))\(\left\)(k+7\(\right\))$
• B. $\(\left\)(k-7\(\right\))\(\left\)(k-7\(\right\))$
• C. $k\(\left\)(k-49\(\right\))$
• D. $\(\left\)(k-49\(\right\))\(\left\)(k+49\(\right\))$

Answer: (A)

Verified step by step guidance

1. Recognize that the problem involves the Difference of Squares, which is a special factoring pattern. The general formula is \(a^2 - b^2 = (a - b)(a + b)\).
2. Identify the two terms in the expression that are perfect squares. For example, if the expression is \(x^2 - 9\), then \(x^2\) and \$9\( are perfect squares because \)x^2 = (x)^2\( and \)9 = (3)^2$.
3. Rewrite the expression explicitly as a difference of squares, such as \(a^2 - b^2\), where \(a\) and \(b\) are the square roots of the two terms.
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.