Question

multiply.
(4a + 5b)(7a + 2b)
simplify your answer.

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$(4a)(7a) + (4a)(2b) + (5b)(7a) + (5b)(2b)$

Step2: Multiply the monomials

Calculate each product:
$28a^2 + 8ab + 35ab + 10b^2$

Step3: Combine like terms

Add the $ab$ terms:
$28a^2 + (8ab + 35ab) + 10b^2 = 28a^2 + 43ab + 10b^2$

Answer:

$28a^2 + 43ab + 10b^2$