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