Questions: Factor the following binomial completely. 81-x^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 81-x^2= B. 81-x^2 is prime.

Factor the following binomial completely. 81-x^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 81-x^2= B. 81-x^2 is prime.
Transcript text: Factor the following binomial completely. \[ 81-x^{2} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $81-x^{2}=$ $\square$ B. $81-x^{2}$ is prime.
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Solution

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Solution Steps

Step 1: Identify the Form

The given expression is in the form of \(a^2 - b^2\), where \(a = 9\) and \(b = x\).

Step 2: Apply the Difference of Squares Formula

The difference of squares formula states that \(a^2 - b^2 = (a + b)(a - b)\).

Step 3: Substitute \(a\) and \(b\) into the Formula

Substituting \(a = 9\) and \(b = x\) into the formula gives us \(a^2 - b^2 = (9 + x)(9 - x)\).

Final Answer:

The factorized form of \(a^2 - b^2\) is \( (9 + x)(9 - x) \).

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