Question

Use distributive property to rewrite the polynomial (x+8)(x-2).
□x²+□x+□

Answer 1

To rewrite the polynomial \((x + 8)(x - 2)\) using the distributive property (also known as the FOIL method for binomials), we will distribute each term in the first binomial to each term in the second binomial:

\[
(x + 8)(x - 2) = x(x) + x(-2) + 8(x) + 8(-2)
\]

Now, performing the multiplication step by step:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-2) = -2x\)
3. \(8 \cdot x = 8x\)
4. \(8 \cdot (-2) = -16\)

Now, combine all the terms together:

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

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

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

So, the polynomial rewritten is:

\[
\boxed{x^2 + 6x - 16}
\]