Polynomials practice
Factor twelve sums and differences of cubes completely. Choose common variable factors, displayed leading coefficients, or mixed practice with exact complete products.
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Factor each sum or difference of cubes completely.
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Customize this worksheetExtract the complete numerical and variable greatest common factor before applying a cube identity. The remaining binomial must contain two exact cubes.
Use A³ + B³ = (A + B)(A² − AB + B²) and A³ − B³ = (A − B)(A² + AB + B²). Multiply the complete product, including its GCF, to check the original two terms.
Learning objective
Extract the complete greatest common factor, then apply the sum or difference of cubes identity.
Worked example
2x(x − 3)(x² + 3x + 9).
Extract 2x to get x³ − 27. Then use the difference-of-cubes identity.
Teaching notes
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Choose the cube structures to practice. Answer editions show the complete factorization for each problem.
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