Question

Use the Distributive property to rewrite the polynomial (x+8) (x-2).
□x²+□x+□

Answer 1

To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we need to multiply each term in the first binomial by each term in the second binomial.

Here’s the step-by-step calculation:

1. **First terms**: Multiply the first terms in each binomial:
\[
x \cdot x = x^2
\]

2. **Outer terms**: Multiply the outer terms:
\[
x \cdot (-2) = -2x
\]

3. **Inner terms**: Multiply the inner terms:
\[
8 \cdot x = 8x
\]

4. **Last terms**: Multiply the last terms in each binomial:
\[
8 \cdot (-2) = -16
\]

Now, we combine all these results:
\[
x^2 - 2x + 8x - 16
\]

Next, combine the like terms \(-2x + 8x\):
\[
x^2 + 6x - 16
\]

So, the polynomial \((x + 8)(x - 2)\) rewritten using the Distributive Property is:
\[
x^2 + 6x - 16
\]

Thus, filling in the blanks as requested:
□x² + □x + □ would be:
1. \(1\) for the \(x^2\) coefficient
2. \(6\) for the \(x\) coefficient
3. \(-16\) as the constant term.

So the answer is:
1. 1, 6, -16.