8
AssignmentMultiple Choice

Sum and Difference of Two Cubes

Question 8 • AZ-Common Core Algebra II A

Factor t12 – r3s15.

Answer
A
(t4 – rs5)(t8 – rs5t4 – r2s10)
B
(t4 – rs5)(t8 + rs5t4 + r2s10)
C
(t9 – rs12)(t18 + rs12t9 + r2s24)
D
(t4 + rs5)(t8 – rs5t4 + r2s10)

Explanation

Write the expression as (t⁴)³ − (rs⁵)³. Use the difference-of-cubes rule, a³ − b³ = (a − b)(a² + ab + b²), with a = t⁴ and b = rs⁵. This gives (t⁴ − rs⁵)(t⁸ + rs⁵t⁴ + r²s¹⁰), which is choice B.

AI-written and checked against the verified answer.