Question

simplify the following expression.
(4x - 8)(4x + 8)

a. 16x² + 64x - 64
b. 16x² - 64
c. 16x² - 16
d. 16x² - 64x - 64

Explanation:

Step1: Identify the formula

The expression \((4x - 8)(4x + 8)\) is in the form of \((a - b)(a + b)\), which is a difference of squares. The formula for the difference of squares is \((a - b)(a + b)=a^{2}-b^{2}\).
Here, \(a = 4x\) and \(b = 8\).

Step2: Apply the formula

First, calculate \(a^{2}\):
\(a^{2}=(4x)^{2}=4^{2}\times x^{2}=16x^{2}\)
Then, calculate \(b^{2}\):
\(b^{2}=8^{2} = 64\)
Using the difference of squares formula \((a - b)(a + b)=a^{2}-b^{2}\), we substitute \(a^{2}=16x^{2}\) and \(b^{2} = 64\) to get:
\((4x - 8)(4x + 8)=16x^{2}-64\)

Answer:

B. \(16x^{2}-64\)