Question

question
factor completely.
81 - 4x²

Explanation:

Step1: Identify the form

The expression \(81 - 4x^2\) is a difference of squares, which has the form \(a^2 - b^2\), where \(a^2 = 81\) and \(b^2 = 4x^2\).

Step2: Find a and b

From \(a^2 = 81\), we get \(a = 9\) (since \(9^2 = 81\)). From \(b^2 = 4x^2\), we get \(b = 2x\) (since \((2x)^2 = 4x^2\)).

Step3: Apply difference of squares formula

The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\). Substituting \(a = 9\) and \(b = 2x\) into the formula, we get \((9 + 2x)(9 - 2x)\).

Answer:

\((9 + 2x)(9 - 2x)\)