Question

find the product. simplify your answer.
(4m - 3)(4m + 3)

Explanation:

Step1: Identify the formula

The expression \((4m - 3)(4m + 3)\) is in the form of \((a - b)(a + b)\), which follows the difference of squares formula: \((a - b)(a + b)=a^2 - b^2\). Here, \(a = 4m\) and \(b = 3\).

Step2: Apply the formula

Substitute \(a = 4m\) and \(b = 3\) into the formula. First, calculate \(a^2=(4m)^2 = 16m^2\) (using the power of a product rule: \((ab)^n=a^n b^n\), so \((4m)^2 = 4^2\times m^2=16m^2\)). Then, calculate \(b^2 = 3^2=9\). Now, using the difference of squares formula, we get \(a^2 - b^2=16m^2-9\).

Answer:

\(16m^2 - 9\)