Here's the step-by-step process:
Given expression: (4y - 4)(-y^2 - 3y - 2)
Step 1: Distribute 4y to each term inside the second parentheses:
= 4y(-y^2) - 4y(-3y) - 4y(-2)
= -4y^3 + 12y^2 + 8y
Step 2: Distribute -4 to each term inside the second parentheses:
= -4(-y^2) - (-4)(-3y) - (-4)(-2)
= 4y^2 + 12y + 8
Step 3: Combine like terms:
= -4y^3 + 4y^2 + 12y^2 + 12y + 8y
= -4y^3 + 16y^2 + 12y
So, the simplified product is: -4y^3 + 16y^2 + 12y.
