Question

find the product. simplify your answer. (2y + 1)(-y² + y - 2)

Explanation:

Step1: Distribute \(2y\) to each term

\(2y \times (-y^2) + 2y \times y + 2y \times (-2) = -2y^3 + 2y^2 - 4y\)

Step2: Distribute \(1\) to each term

\(1 \times (-y^2) + 1 \times y + 1 \times (-2) = -y^2 + y - 2\)

Step3: Combine like terms

\((-2y^3 + 2y^2 - 4y) + (-y^2 + y - 2) = -2y^3 + (2y^2 - y^2) + (-4y + y) - 2 = -2y^3 + y^2 - 3y - 2\)

Answer:

\(-2y^3 + y^2 - 3y - 2\)