Question

factor the following binomial. 81 - 49x² (? + x)( - x)

Explanation:

Step1: Identify the difference of squares

The binomial \(81 - 49x^2\) is a difference of squares, which can be written in the form \(a^2 - b^2\), where \(a^2 = 81\) and \(b^2 = 49x^2\).

Step2: Find the square roots

The square root of \(81\) is \(9\), so \(a = 9\). The square root of \(49x^2\) is \(7x\), so \(b = 7x\).

Step3: Apply the 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 \(b = 7x\) into the formula, we get \((9 + 7x)(9 - 7x)\).

Answer:

\((9 + 7x)(9 - 7x)\)