Question

find the product. simplify your answer. (2f + 2)(f + 1)

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
$(2r + 2)(r + 1) = 2r \cdot r + 2r \cdot 1 + 2 \cdot r + 2 \cdot 1$
Simplify each product:
$= 2r^2 + 2r + 2r + 2$

Step2: Combine like terms

Add the middle terms ($2r + 2r$):
$2r^2 + (2r + 2r) + 2 = 2r^2 + 4r + 2$

(Optional: Factor out a 2 for further simplification, though the expanded form is also simplified:
$2(r^2 + 2r + 1) = 2(r + 1)^2$)

Answer:

$2r^2 + 4r + 2$ (or $2(r + 1)^2$)