Factor the following as the difference of two squares. Be sure to factor completely.
\[
36 a^{2}-25 b^{2}=
\]

Answer

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Answer

\(\boxed{(6a + 5b)(6a - 5b)}\)

Steps

Step 1 ：Identify \(A^2\) and \(B^2\) in the given expression \(36 a^{2} - 25 b^{2}\)

Step 2 ：Find the square roots of \(A^2\) and \(B^2\), \(A = \sqrt{36 a^{2}} = 6a\) and \(B = \sqrt{25 b^{2}} = 5b\)

Step 3 ：Apply the difference of two squares formula \((A + B)(A - B)\)

Step 4 ：\(\boxed{(6a + 5b)(6a - 5b)}\)