Factoring Polynomials: Sum and Difference of Cubes
Question 4 • Common Core Algebra I B-IC
What is the factored form of 125x6 – 8?
Answer
A
(5x2 – 2)(25x4 – 10x2 – 4)
B
(5x2 – 2)(25x4 – 10x2 + 4)
C
(5x2 – 2)(25x4 + 10x2 + 4)
D
(5x2 – 2)(25x4 + 10x2 – 4)
Explanation
Recognize 125x⁶ − 8 as a difference of cubes: (5x²)³ − 2³. Use a³ − b³ = (a − b)(a² + ab + b²), giving (5x² − 2)(25x⁴ + 10x² + 4). This matches choice C.
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