Question

1. expand and simplify.

a) $(3y - 2)(y^2 + y - 8)$

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(3y\) with each term in \((y^2 + y - 8)\) and \(-2\) with each term in \((y^2 + y - 8)\):
\(3y \times y^2 + 3y \times y - 3y \times 8 - 2 \times y^2 - 2 \times y + 2 \times 8\)

Step2: Simplify each product

Calculate each term:
\(3y^3 + 3y^2 - 24y - 2y^2 - 2y + 16\)

Step3: Combine like terms

Combine \(3y^2\) and \(-2y^2\), \(-24y\) and \(-2y\):
\(3y^3 + (3y^2 - 2y^2) + (-24y - 2y) + 16 = 3y^3 + y^2 - 26y + 16\)

Answer:

\(3y^3 + y^2 - 26y + 16\)