Complete the table to find the product of (5y^2−6y)(7y^7−y^3) . Provide your answer in descending order of exponents.(2 points)

Question

Apply the Product Rule of Exponents xa⋅xb=xa+b to find the product of −6y⋅7y2. Apply the Product Rule of Exponents xa⋅xb=xa+b to find the product of 5y2⋅(−y3). Apply the Product Rule of Exponents xa⋅xb=xa+b to find the product of −6y⋅(−y3). Apply the Product Rule of Exponents xa⋅xb=xa+b to complete the table.

Answer 1

To find the product of the polynomials \( (5y^2 - 6y)(7y^7 - y^3) \), we'll use the distributive property (also known as the FOIL method for binomials) to compute each term step by step. We'll multiply each term in the first polynomial by each term in the second polynomial.

1. Calculate each term:

   • First, we will find: \[ 5y^2 \cdot 7y^7 = 35y^{2+7} = 35y^9 \]

   • Next, let's compute: \[ 5y^2 \cdot (-y^3) = -5y^{2+3} = -5y^5 \]

   • Now, for: \[ -6y \cdot 7y^7 = -42y^{1+7} = -42y^8 \]

   • Next, we calculate: \[ -6y \cdot (-y^3) = 6y^{1+3} = 6y^4 \]

2. Now, we can sum all these products together: \[ 35y^9 - 42y^8 - 5y^5 + 6y^4 \]

3. Combine the results to express the final polynomial in descending order of exponents: \[ 35y^9 - 42y^8 - 5y^5 + 6y^4 \]

Thus, the completed product in descending order of exponents is:

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