Question

Use distribute property to rewrite the polynomial (x+8)(x-2)

Answer 1

To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property, we will distribute each term in the first parentheses by each term in the second parentheses.

1. Distribute \(x\) across \((x - 2)\):
\[
x \cdot x + x \cdot (-2) = x^2 - 2x
\]

2. Distribute \(8\) across \((x - 2)\):
\[
8 \cdot x + 8 \cdot (-2) = 8x - 16
\]

Now, combine all the terms:
\[
x^2 - 2x + 8x - 16
\]

Combine the like terms \(-2x\) and \(8x\):
\[
x^2 + 6x - 16
\]

Thus, the rewritten polynomial is:
\[
x^2 + 6x - 16
\]