Answer:
x³ + 7x² + 15x + 9
Step-by-step explanation:
Given that the volume (V) of a rectangular pyramid is
V = [tex]\frac{1}{3}[/tex] A h ( A is the area of base and h the height ), then
V = [tex]\frac{1}{3}[/tex] (3x² + 12x + 9)(x + 3) ← factor out 3 from A
= [tex]\frac{1}{3}[/tex] × 3(x² + 4x + 3)(x + 3)
= (x² + 4x + 3)(x + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x² (x + 3) + 4x(x + 3) + 3(x + 3) ← distribute parenthesis
= x³ + 3x² + 4x² + 12x + 3x + 9 ← collect like terms
= x³ + 7x² + 15x + 9
Thus the expression for the volume is
V = x³ + 7x² + 15x + 9
