To apply the Distributive Property to the polynomial \((x+8)(x−2)\), you need to distribute each term in the first binomial by each term in the second binomial. Here’s how you can do it step by step:
-
Distribute \(x\) in \((x + 8)\):
- \(x \cdot x = x^2\)
- \(x \cdot (-2) = -2x\)
-
Distribute \(8\) in \((x + 8)\):
- \(8 \cdot x = 8x\)
- \(8 \cdot (-2) = -16\)
-
Combine all the terms together: \[ x^2 - 2x + 8x - 16 \]
-
Combine like terms (\(-2x\) and \(8x\)): \[ x^2 + 6x - 16 \]
Now, you can fill in the blanks for your polynomial:
\(x^2 + 6x - 16\)
So the answer is:
- \(x^2 + 6x - 16\)