Question
Use the Distributive Property to rewrite the polynomial (x + 8) (x − 2).
___ x^2 + 6x + ____
___ x^2 + 6x + ____
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 proceed as follows:
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 \(-2x + 8x\):
\[
x^2 + 6x - 16
\]
So, in the structure you provided:
\[
x^2 + 6x + (-16)
\]
The completed polynomial is \(x^2 + 6x - 16\).
Thus, filling in the blanks:
___ 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 \(-2x + 8x\):
\[
x^2 + 6x - 16
\]
So, in the structure you provided:
\[
x^2 + 6x + (-16)
\]
The completed polynomial is \(x^2 + 6x - 16\).
Thus, filling in the blanks:
___ x^2 + 6x + **(-16)**