Asked by Nanika Zoldyck
Complete the table to find the product of (5y2−6y)(7y7−y3)
. Provide your answer in descending order of exponents.(2 points)
. Provide your answer in descending order of exponents.(2 points)
Answers
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Answered by
GPT-4o mini
To find the product of the two polynomials \((5y^2 - 6y)(7y^7 - y^3)\), we will use the distributive property (also known as the FOIL method for binomials). We will multiply each term in the first polynomial by each term in the second polynomial.
1. **Multiply \(5y^2\) by each term in \(7y^7 - y^3\)**:
- \(5y^2 \cdot 7y^7 = 35y^{9}\)
- \(5y^2 \cdot (-y^3) = -5y^{5}\)
2. **Multiply \(-6y\) by each term in \(7y^7 - y^3\)**:
- \(-6y \cdot 7y^7 = -42y^{8}\)
- \(-6y \cdot (-y^3) = 6y^{4}\)
Now, combine all these products together:
\[
35y^{9} - 42y^{8} - 5y^{5} + 6y^{4}
\]
Next, we can arrange the terms in descending order of exponents:
\[
35y^{9} - 42y^{8} - 5y^{5} + 6y^{4}
\]
So the final result of the product \((5y^2 - 6y)(7y^7 - y^3)\) is:
\[
\boxed{35y^{9} - 42y^{8} - 5y^{5} + 6y^{4}}
\]
1. **Multiply \(5y^2\) by each term in \(7y^7 - y^3\)**:
- \(5y^2 \cdot 7y^7 = 35y^{9}\)
- \(5y^2 \cdot (-y^3) = -5y^{5}\)
2. **Multiply \(-6y\) by each term in \(7y^7 - y^3\)**:
- \(-6y \cdot 7y^7 = -42y^{8}\)
- \(-6y \cdot (-y^3) = 6y^{4}\)
Now, combine all these products together:
\[
35y^{9} - 42y^{8} - 5y^{5} + 6y^{4}
\]
Next, we can arrange the terms in descending order of exponents:
\[
35y^{9} - 42y^{8} - 5y^{5} + 6y^{4}
\]
So the final result of the product \((5y^2 - 6y)(7y^7 - y^3)\) is:
\[
\boxed{35y^{9} - 42y^{8} - 5y^{5} + 6y^{4}}
\]
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