7y^2-y-1)(2y^2-6y-5)
To multiply these two quadratic expressions, we will use the distributive property.
(7y^2 - y - 1)(2y^2 - 6y - 5)
First, distribute the first term in the first expression to all terms in the second expression:
7y^2 * 2y^2 - 7y^2 * 6y - 7y^2 * 5
This gives us:
14y^4 - 42y^3 - 35y^2
Next, distribute the second term in the first expression to all terms in the second expression:
-y * 2y^2 - y * -6y - y * -5
This gives us:
-2y^3 + 6y^2 + 5y
Finally, distribute the third term in the first expression to all terms in the second expression:
-1 * 2y^2 - 1 * -6y - 1 * -5
This gives us:
-2y^2 + 6y + 5
Now, sum up all the terms:
14y^4 - 42y^3 - 35y^2 - 2y^3 + 6y^2 + 5y - 2y^2 + 6y + 5
Combine like terms:
14y^4 - 44y^3 - 31y^2 + 11y + 5
Therefore, the product of (7y^2 - y - 1)(2y^2 - 6y - 5) is 14y^4 - 44y^3 - 31y^2 + 11y + 5.