Question

find the product. simplify your answer.
(d + 4)(d² + 3d + 4)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(d\) by each term in \((d^2 + 3d + 4)\) and \(4\) by each term in \((d^2 + 3d + 4)\):
\(d \cdot d^2 + d \cdot 3d + d \cdot 4 + 4 \cdot d^2 + 4 \cdot 3d + 4 \cdot 4\)

Step2: Simplify each term

Calculate the products:
\(d^3 + 3d^2 + 4d + 4d^2 + 12d + 16\)

Step3: Combine like terms

Combine \(3d^2\) and \(4d^2\), \(4d\) and \(12d\):
\(d^3 + (3d^2 + 4d^2) + (4d + 12d) + 16 = d^3 + 7d^2 + 16d + 16\)

Answer:

\(d^3 + 7d^2 + 16d + 16\)