use the distributive property to rewrite the polynomial (x+8)(x-2)

Answer 1

To use the distributive property to rewrite the polynomial \((x + 8)(x - 2)\), we distribute each term in the first binomial by each term in the second binomial.

Here’s how it works step-by-step:

1. Distribute \(x\): \[ x \cdot x + x \cdot (-2) = x^2 - 2x \]

2. Distribute \(8\): \[ 8 \cdot x + 8 \cdot (-2) = 8x - 16 \]

3. Now, combine all the terms together: \[ x^2 - 2x + 8x - 16 \]

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

So, the polynomial \((x + 8)(x - 2)\) can be rewritten as:

\[ x^2 + 6x - 16 \]