Question

question 22 of 25
what is the factorization of the expression below?
$4x^2 - 81$

a. $(2x - 9)(2x - 9)$
b. $(4x + 9)(x - 9)$
c. $(4x - 9)(x - 9)$
d. $(2x + 9)(2x - 9)$

Explanation:

Step1: Identify the formula

The expression \(4x^2 - 81\) is a difference of squares. The formula for factoring a difference of squares is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Rewrite the terms as squares

We can rewrite \(4x^2\) as \((2x)^2\) and \(81\) as \(9^2\). So the expression becomes \((2x)^2-9^2\).

Step3: Apply the difference of squares formula

Using the formula \(a^2 - b^2=(a + b)(a - b)\) with \(a = 2x\) and \(b = 9\), we get \((2x + 9)(2x - 9)\).

Answer:

D. \((2x + 9)(2x - 9)\)