Question

find the product. simplify your answer.
(q + 4)(2q + 4)

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
\( (q + 4)(2q + 4) = q \cdot 2q + q \cdot 4 + 4 \cdot 2q + 4 \cdot 4 \)

Step2: Simplify each term

Calculate the products:
\( q \cdot 2q = 2q^2 \), \( q \cdot 4 = 4q \), \( 4 \cdot 2q = 8q \), \( 4 \cdot 4 = 16 \)

Step3: Combine like terms

Add the \( q \)-terms: \( 4q + 8q = 12q \)
So the expression becomes \( 2q^2 + 12q + 16 \)

Answer:

\( 2q^2 + 12q + 16 \)