Question

use the distributive property to rewrite the polynomial (x+8) (x-2)

Answer 1

To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property, you will multiply each term in the first binomial by each term in the second binomial. Here’s how it’s done step-by-step:

1. Distribute \(x\) in \((x + 8)\) to both terms in \((x - 2)\):
\[
x \cdot x + x \cdot (-2) = x^2 - 2x
\]

2. Distribute \(8\) in \((x + 8)\) to both terms in \((x - 2)\):
\[
8 \cdot x + 8 \cdot (-2) = 8x - 16
\]

3. Combine all the terms from the two distributions:
\[
x^2 - 2x + 8x - 16
\]

4. Combine like terms:
\[
x^2 + 6x - 16
\]

The polynomial \((x + 8)(x - 2)\) rewritten using the distributive property is:
\[
x^2 + 6x - 16
\]