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

Question

.(2 points)
x2+
x+
Incorrect

Remember that a coefficient of 1 on a variable is typically not written.
Remember that this expression will generate multiple x terms.
Remember that a negative value times a positive value will equal a negative value.

Answer 1

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

1. Distribute \(x\) to both terms in the second parenthesis: \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]

2. Distribute \(8\) to both terms in the second parenthesis: \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]

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

4. Combine like terms: \[ x^2 + (8x - 2x) - 16 = x^2 + 6x - 16 \]

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