Question

Use the Distributive Property to rewrite the polynomial (x + 8)(x - 2)

Box x ^ 2 + Box x+ Box

Answer 1

To use the Distributive Property to rewrite the polynomial \((x + 8)(x - 2)\), we will distribute each term in the first binomial \((x + 8)\) to each term in the second binomial \((x - 2)\).

Here are the steps:

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

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

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

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

Now, we can fill in the boxes:

\[
\text{Box} \, x^2 + \text{Box} \, 6x + \text{Box} \, (-16)
\]

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

The filled-in boxes will be:

- Box for \(x^2\): 1 (since it can be written as \(1x^2\))
- Box for \(6x\): 6
- Box for \(-16\): -16