Question

multiply. (4b - 5)(-5b + 8) simplify your answer.

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
\((4b - 5)(-5b + 8)=4b\times(-5b)+4b\times8+(-5)\times(-5b)+(-5)\times8\)

Step2: Simplify each product

Calculate each term:
\(4b\times(-5b)= -20b^2\)
\(4b\times8 = 32b\)
\((-5)\times(-5b)=25b\)
\((-5)\times8=-40\)

Step3: Combine like terms

Combine the \(b\) terms:
\(-20b^2+(32b + 25b)-40=-20b^2 + 57b-40\)

Answer:

\(-20b^2 + 57b - 40\)