(9y^2+2)(y^2-y-1)
(9y^2+2)(y^2-y-1)
use distributive property
9y^2(y^2-y-1) + 2(y^2-y-1)
To find the product of the given expression (9y^2+2)(y^2-y-1), we can use the distributive property of multiplication over addition.
Step 1: Expand the expression using the distributive property. Multiply each term in the first expression (9y^2+2) by each term in the second expression (y^2-y-1).
(9y^2+2)(y^2-y-1) = 9y^2(y^2-y-1) + 2(y^2-y-1)
Step 2: Continue expanding the expression by multiplying each term in the parentheses by the corresponding term in (9y^2+2).
First, let's distribute 9y^2 to each term in the parentheses:
9y^2(y^2-y-1) = 9y^2 * y^2 - 9y^2 * y - 9y^2 * 1
Simplifying this will give us:
9y^4 - 9y^3 - 9y^2
Next, distribute 2 to each term in the parentheses:
2(y^2-y-1) = 2 * y^2 - 2 * y - 2 * 1
Simplifying this will give us:
2y^2 - 2y - 2
Step 3: Combine the two simplified expressions obtained from the previous steps.
Putting it all together, we have:
(9y^2+2)(y^2-y-1) = 9y^4 - 9y^3 - 9y^2 + 2y^2 - 2y - 2
Step 4: Simplify the expression by combining like terms.
Combining like terms, we get:
9y^4 - 9y^3 - 7y^2 - 2y - 2
Therefore, the product of (9y^2+2)(y^2-y-1) is 9y^4 - 9y^3 - 7y^2 - 2y - 2.