16
AssignmentMultiple Choice

Sum and Difference of Two Cubes

Question 16 • NJ-Algebra II

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

Recognize a difference of cubes: t¹² = (t⁴)³ and r³s¹⁵ = (rs⁵)³. Using a³ − b³ = (a − b)(a² + ab + b²), with a = t⁴ and b = rs⁵, gives (t⁴ − rs⁵)(t⁸ + rs⁵t⁴ + r²s¹⁰). This matches choice B.

AI-written and checked against the verified answer.

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