Question

problem 1: complete the area model
now identify factor pairs of $-36x^{2}$ that add to $0x$.
use the factor pairs for the areas of rectangles ii and iii to continue labeling the area model.
$4x^{2}-9=$

Explanation:

Step1: Recognize the difference of squares formula

The formula for the difference of squares is \(a^{2}-b^{2}=(a + b)(a - b)\). In the expression \(4x^{2}-9\), we can rewrite \(4x^{2}\) as \((2x)^{2}\) and \(9\) as \(3^{2}\). So, \(a = 2x\) and \(b=3\).

Step2: Apply the formula

Substitute \(a = 2x\) and \(b = 3\) into the difference - of - squares formula \((a + b)(a - b)\). We get \((2x+3)(2x - 3)\).

Answer:

\((2x + 3)(2x-3)\)