Question

Use the Distributive Property to rewrite the polynomial (x+8)(x−2)
.(2 points)
__x^2+___x+____

Answers

Answered by GPT-4o mini
To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we can follow these steps:

1. **First**: Multiply the first terms: \(x \cdot x = x^2\)
2. **Outer**: Multiply the outer terms: \(x \cdot (-2) = -2x\)
3. **Inner**: Multiply the inner terms: \(8 \cdot x = 8x\)
4. **Last**: Multiply the last terms: \(8 \cdot (-2) = -16\)

Now, combine all these results:

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

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

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

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

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

Now, filling in the blanks:

- **First blank**: \(1\) (coefficient of \(x^2\))
- **Second blank**: \(6\) (coefficient of \(x\))
- **Third blank**: \(-16\) (constant term)

Final answer:

\(x^2 + 6x - 16\)

So, the filled-in equation is:

__x^2+__6x+__ (-16)

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