Question

using the distributive property rewrite the polynominal (x+8)(x-2)

Answer 1

To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property, we apply the concept of distributing each term in the first parentheses to each term in the second parentheses:

1. Multiply \(x\) by \(x\):
\[
x \cdot x = x^2
\]

2. Multiply \(x\) by \(-2\):
\[
x \cdot -2 = -2x
\]

3. Multiply \(8\) by \(x\):
\[
8 \cdot x = 8x
\]

4. Multiply \(8\) by \(-2\):
\[
8 \cdot -2 = -16
\]

Now, combine all these results:

\[
x^2 - 2x + 8x - 16
\]

Next, combine the like terms \(-2x\) and \(8x\):

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

So, the polynomial \((x + 8)(x - 2)\) rewritten using the distributive property is:

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