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

Question

.(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: \[ x^2 + 6x - 16 \]