Question

(b + 3)(b² + 2b + 1) options: b³+5b²+7b+3; b³+6b²+6b+3; 4b³+8b²+3b; 3b³+6b²+3b

Explanation:

Step1: Distribute $b$ to the quadratic

$b(b^2 + 2b + 1) = b^3 + 2b^2 + b$

Step2: Distribute $3$ to the quadratic

$3(b^2 + 2b + 1) = 3b^2 + 6b + 3$

Step3: Combine like terms

$(b^3 + 2b^2 + b) + (3b^2 + 6b + 3) = b^3 + (2b^2+3b^2) + (b+6b) + 3$

Answer:

$b^3+5b^2+7b+3$