Factor.
\[
81 w^{2}-4 v^{2}
\]

Answer

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Answer

The factored form of the expression \(81 w^{2}-4 v^{2}\) is \(\boxed{(-2v + 9w)(2v + 9w)}\).

Steps

Step 1 ：This is a difference of squares problem. The difference of squares formula is a^2 - b^2 = (a - b)(a + b).

Step 2 ：In this case, a = sqrt(81w^2) = 9w and b = sqrt(4v^2) = 2v.

Step 3 ：So we can apply the formula to factor the expression.

Step 4 ：The factored form of the expression \(81 w^{2}-4 v^{2}\) is \(\boxed{(-2v + 9w)(2v + 9w)}\).