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Sum and Difference of Two Cubes

Question 8 • AZ-Common Core Algebra II A

Choose the expressions that are sums or differences of two cubes.

Answer
A
64 + a12b51
B
–t6 + u3v21
C
8h45 – k15
D
75 – n3p6
E
–27 – xz9

Explanation

A sum or difference of two cubes has two terms, each of which is a perfect cube. In A, 64 = 4³ and a¹²b⁵¹ = (a⁴b¹⁷)³. In B, −t⁶ = (−t²)³ and u³v²¹ = (uv⁷)³; in C, 8h⁴⁵ = (2h¹⁵)³ and k¹⁵ = (k⁵)³. D has 75, which is not a perfect cube, and E has x with exponent 1, so those terms are not perfect cubes.

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