Sum and Difference of Cubes Practice Test

Factor and apply the identities for a³+b³ and a³−b³.

Sum and Difference of Cubes Practice Test

This test has 20 questions

About This "Sum and Difference of Cubes Practice Test"

This test develops both recognition and flexible use of the two cubic identities.

"Perfect cubes, sign patterns, coefficients, two variables, GCF first, real cube roots, expansion, and symmetric identities."

Skills Covered

Perfect cubes, sign patterns, coefficients, two variables, GCF first, real cube roots, expansion, and symmetric identities.

Key Ideas

  1. a³+b³=(a+b)(a²−ab+b²).
  2. a³−b³=(a−b)(a²+ab+b²).
  3. The quadratic factor is not another binomial cube.
  4. Always remove a GCF before applying the identity.

Common Mistakes to Avoid

Remember SOAP: Same sign in the binomial, Opposite middle sign, Always Positive last term.

Practice Format

Each question has four answer choices. The explanation shows the method, completes the work, states the conclusion, and explains why every distractor is incorrect.