Question
Explain the following text primarily based on the surrounding page content: Use the Distributive Property to rewrite the polynomial (x+8)(2x−2) ( 𝑥 + 8 ) ( 2 𝑥 − 2 ) .(2 points) x2+ 𝑥 2 + x+ 𝑥 +
Answers
GPT-4o mini
The text is focused on the use of the Distributive Property to manipulate a polynomial expression represented by the product of two binomials: (x + 8)(2x - 2).
To use the Distributive Property, also known as the FOIL method (First, Outer, Inner, Last), we expand the expression as follows:
1. **First**: Multiply the first terms in each binomial:
\( x \cdot 2x = 2x^2 \)
2. **Outer**: Multiply the outer terms:
\( x \cdot (-2) = -2x \)
3. **Inner**: Multiply the inner terms:
\( 8 \cdot 2x = 16x \)
4. **Last**: Multiply the last terms:
\( 8 \cdot (-2) = -16 \)
Now, we combine all these results:
\( 2x^2 - 2x + 16x - 16 \)
Next, we simplify by combining like terms:
\( 2x^2 + (16x - 2x) - 16 = 2x^2 + 14x - 16 \)
So, the final expression after applying the Distributive Property to (x + 8)(2x - 2) is:
\( 2x^2 + 14x - 16 \).
Based on how the provided text is structured, it seems to indicate that there might be a typographical error with "(x+8)(2x−2) ( 𝑥 + 8 ) ( 2 𝑥 − 2 ).(2 points) x2+ 𝑥 2 + x+ 𝑥 +". The end of the text may have meant to present the final expression or provide a point breakdown for a problem, but it is incomplete or garbled.
In summary, the Distributive Property allows us to expand the product of binomials efficiently, leading to a polynomial that can be simplified to show its combined terms.
To use the Distributive Property, also known as the FOIL method (First, Outer, Inner, Last), we expand the expression as follows:
1. **First**: Multiply the first terms in each binomial:
\( x \cdot 2x = 2x^2 \)
2. **Outer**: Multiply the outer terms:
\( x \cdot (-2) = -2x \)
3. **Inner**: Multiply the inner terms:
\( 8 \cdot 2x = 16x \)
4. **Last**: Multiply the last terms:
\( 8 \cdot (-2) = -16 \)
Now, we combine all these results:
\( 2x^2 - 2x + 16x - 16 \)
Next, we simplify by combining like terms:
\( 2x^2 + (16x - 2x) - 16 = 2x^2 + 14x - 16 \)
So, the final expression after applying the Distributive Property to (x + 8)(2x - 2) is:
\( 2x^2 + 14x - 16 \).
Based on how the provided text is structured, it seems to indicate that there might be a typographical error with "(x+8)(2x−2) ( 𝑥 + 8 ) ( 2 𝑥 − 2 ).(2 points) x2+ 𝑥 2 + x+ 𝑥 +". The end of the text may have meant to present the final expression or provide a point breakdown for a problem, but it is incomplete or garbled.
In summary, the Distributive Property allows us to expand the product of binomials efficiently, leading to a polynomial that can be simplified to show its combined terms.