Question

Use the Distributive Property to rewrite the polynomial left parenthesis x plus 8 right parenthesis left parenthesis x minus 2 right parenthesis

Answer 1

this is wrong there are two addtions blank x^2 + blank x + blank

Answer 2

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

Here's how to do it step by step:

1. Distribute \(x\) from the first parenthesis:
- \(x \cdot x = x^2\)
- \(x \cdot (-2) = -2x\)

2. Distribute \(8\) from the first parenthesis:
- \(8 \cdot x = 8x\)
- \(8 \cdot (-2) = -16\)

Now, we combine all these products together:

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

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:

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

Answer 3

Let’s clarify the distribution step again to fill the blanks correctly for the expression \((x + 8)(x - 2)\).

Using the Distributive Property, we will expand the expression step by step:

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

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

Now, put them together:

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

Combine like terms (\(-2x\) and \(8x\)):

\[
x^2 + (8x - 2x) - 16 = x^2 + 6x - 16
\]

Now, filling in the blanks:

\[
\text{So, } x^2 + 6x - 16 \text{ corresponds to } (x^2 + 6x - 16).
\]

In the format you requested:
- First blank: \(1\) (for \(x^2\))
- Second blank: \(6\) (for \(6x\))
- Third blank: \(-16\) (the constant term)

Thus, we have the completed polynomial:

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

Thank you for your patience, and let me know if you need any further clarification!