Factoring Polynomials: Sum and Difference of Cubes

Question 6 • FL-1200710-Mathematics for College Algebra A

What is 125x9 + 64y12 written as a sum of cubes?

Answer

(

(25x3)3 + (4y4)3

(

(5x3)3 + (16y4)3

(

(25x3)3 + (8y4)3

(

(5x3)3 + (4y4)3

Since 125 = 5³ and x⁹ = (x³)³, the first term is (5x³)³. Also, 64 = 4³ and y¹² = (y⁴)³, so the sum is (5x³)³ + (4y⁴)³, which is choice D.

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