Complete the table to find the product of (5y2−6y)(7y7−y3)

Question

. Provide your answer in descending order of exponents.(2 points)
$$
Remaining Attempts : 3
Skip to navigation

Answer 1

To find the product of the polynomials \((5y^2 - 6y)(7y^7 - y^3)\), we will use the distributive property (also known as the FOIL method for binomials).

Let's multiply each term in the first polynomial by each term in the second polynomial:

1. \(5y^2 \cdot 7y^7 = 35y^{2+7} = 35y^9\)
2. \(5y^2 \cdot (-y^3) = -5y^{2+3} = -5y^5\)
3. \(-6y \cdot 7y^7 = -42y^{1+7} = -42y^8\)
4. \(-6y \cdot (-y^3) = 6y^{1+3} = 6y^4\)

Now, let's combine all the results together:

\[ 35y^9 - 42y^8 - 5y^5 + 6y^4 \]

Now, let's write the terms in descending order of exponents:

\[ 35y^9 - 42y^8 - 5y^5 + 6y^4 \]

This is the final answer for the product of \((5y^2 - 6y)(7y^7 - y^3)\).

If you're looking to fill in a table, it can look something like this:

| Term | Exponent | Coefficient | |---------------|----------|-------------| | \(y^9\) | 9 | 35 | | \(y^8\) | 8 | -42 | | \(y^5\) | 5 | -5 | | \(y^4\) | 4 | 6 |

Let me know if you need any more help!