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Factoring Polynomials: Sum and Difference of Cubes

Question 2 • Common Core Algebra I B-IC

Which are sums of perfect cubes? Check all that apply.

Answer
A
8x6 + 27
B
x9 + 1
C
81x3 + 16x6
D
x6 + x3
E
27x9 + x12
F
9x3 + 27x9

Explanation

A sum is a sum of perfect cubes when each term is a cube, using the exponents and coefficients shown. A is (2x²)³ + 3³, B is (x³)³ + 1³, D is (x²)³ + x³, and E is (3x³)³ + (x⁴)³. In C, 81 is not a perfect-cube coefficient, and in F, 9 is not a perfect-cube coefficient, so those are not sums of perfect cubes.

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