Question

Use 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 can distribute each term in the first parentheses to each term in the second parentheses.

Here's how it works 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. Now, combine all the terms from both distributions:
\[
x^2 - 2x + 8x - 16
\]

4. Combine like terms:
\[
x^2 + (8x - 2x) - 16 = x^2 + 6x - 16
\]

So, the polynomial \((x + 8)(x - 2)\) can be rewritten as:
\[
x^2 + 6x - 16
\]