Question

factor the following binomial. 36x² - 49 (?x + )( x - )

Explanation:

Step1: Identify as difference of squares

The given binomial \(36x^2 - 49\) can be written as \((6x)^2 - 7^2\), which is a difference of squares. The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Apply the difference of squares formula

Here, \(a = 6x\) and \(b = 7\). So, factoring \((6x)^2 - 7^2\) using the formula gives \((6x + 7)(6x - 7)\).

Answer:

The filled - in form is \((\boldsymbol{6}x + \boldsymbol{7})(\boldsymbol{6}x - \boldsymbol{7})\)