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.
-
Multiply \(5y^2\) by each term in \(7y^7 - y^3\):
- \(5y^2 \cdot 7y^7 = 35y^{9}\)
- \(5y^2 \cdot (-y^3) = -5y^{5}\)
-
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 answer