To find the product of the polynomials \((5y^2 - 6y)(7y^7 - y^3)\), we will apply the distributive property (also known as the FOIL method for binomials). We will multiply each term from the first polynomial by each term of the second polynomial.
Here are the steps for the multiplication:
-
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, combining all the products, we have: \[ 35y^{9} - 42y^{8} - 5y^{5} + 6y^{4} \]
Next, we will arrange the terms in descending order of exponents:
- \(35y^{9}\)
- \(-42y^{8}\)
- \(-5y^{5}\)
- \(6y^{4}\)
So, the complete expression in descending order is: \[ 35y^{9} - 42y^{8} - 5y^{5} + 6y^{4} \]
No like terms to combine exist, so we retain this product as the final result.
Final Result:
\[ 35y^9 - 42y^8 - 5y^5 + 6y^4 \]
1 answer