Question

multiply.
(a + 4b)(7a - 2b)
simplify your answer.

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
\(a \times 7a + a \times (-2b) + 4b \times 7a + 4b \times (-2b)\)

Step2: Simplify each product

\(7a^2 - 2ab + 28ab - 8b^2\)

Step3: Combine like terms

Combine the middle terms \(-2ab\) and \(28ab\):
\(7a^2 + ( - 2ab + 28ab) - 8b^2 = 7a^2 + 26ab - 8b^2\)

Answer:

\(7a^2 + 26ab - 8b^2\)