Question

find the product. simplify your answer.
(3y + 3)(4y + 4)

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$(3y)(4y) + (3y)(4) + (3)(4y) + (3)(4)$

Step2: Simplify each product

$12y^2 + 12y + 12y + 12$

Step3: Combine like terms

$12y^2 + (12y + 12y) + 12 = 12y^2 + 24y + 12$

Step4: Factor (optional, but simplifies)

Notice $3(4y^2 + 8y + 4)$? Wait, better: factor out 12? Wait, original terms: $3y + 3 = 3(y + 1)$, $4y + 4 = 4(y + 1)$. So rewrite:
$3(y + 1) \cdot 4(y + 1) = 12(y + 1)^2$

Expand $(y + 1)^2 = y^2 + 2y + 1$, so $12(y^2 + 2y + 1) = 12y^2 + 24y + 12$ (matches Step3).

Answer:

$12y^2 + 24y + 12$ (or $12(y + 1)^2$)