Question

factor the following binomial.\\(4x^2 - 9\\)\\((?x + \square)(\square x - \square)\\)

Explanation:

Step1: Identify as difference of squares

The binomial \(4x^2 - 9\) can be written as \((2x)^2 - 3^2\), which is a difference of squares. The formula for factoring a difference of squares \(a^2 - b^2\) is \((a + b)(a - b)\).

Step2: Apply the difference of squares formula

Here, \(a = 2x\) and \(b = 3\). So, factoring \( (2x)^2 - 3^2 \) using the formula gives \((2x + 3)(2x - 3)\).

Answer:

\((\boldsymbol{2}x + \boldsymbol{3})(\boldsymbol{2}x - \boldsymbol{3})\)