Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2)
.(2 points)
x2+
x+
Remaining Attempts

Answer 1

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

1. **First:** Multiply the first terms:
\(x \cdot x = x^2\)

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

3. **Inner:** Multiply the inner terms:
\(8 \cdot x = 8x\)

4. **Last:** Multiply the last terms:
\(8 \cdot (-2) = -16\)

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

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

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

Thus, the final form with the blanks filled in is:
\[
x^2 + 6x - 16
\]