9
QuizMultiple Choice

Polynomials — Test

Question 9 • Algebra 2 with Probability

A cube with side length 5 h squared is stacked on another cube with side length 3 k What is the total volume of the cubes in factored form?

Answer
A
open paren 5 h squared plus 3 k close paren times open paren 25 4th power of h minus 15 h squared k plus 9 k squared close paren
B
open paren 5 h squared plus 3 k close paren cubed
C
open paren 5 h squared close paren cubed plus 3 k cubed
D
open paren 5 h squared plus 3 k close paren times open paren 25 4th power of h plus 15 h squared k plus 9 k squared close paren

Explanation

The volume of a cube is its side length cubed, so the total volume is (5h²)³ + (3k)³. This is a sum of cubes: use a³ + b³ = (a + b)(a² − ab + b²), with a = 5h² and b = 3k. The factored result is (5h² + 3k)(25h⁴ − 15h²k + 9k²), which is choice A.

AI-written and checked against the verified answer.

Previous
Next