10 questions
10th - 12th Grade
Mathematics
Sum/Difference of Cubes is a Grade 10–12 mathematics worksheet focused on factoring polynomial expressions in the form a³ − b³ and a³ + b³. Students answer 10 multiple-choice questions that require them to identify cube roots, choose the correct binomial factor, and match the associated quadratic factor, including expressions such as 8x³ − 1, 27x³ + 8, and 125x³ − 64. This free printable worksheet helps students apply the sum and difference of cubes identities accurately across varied coefficients and signs. The multiple-choice format makes it useful for guided practice, independent review, or a quick check of whether students can distinguish correct factor pairs and fully factor each expression. An answer key is included for efficient checking and feedback.
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WorksheetsAnswer Key
(4x + 5)(16x2 - 20x + 25)
This worksheet covers factoring polynomial sums and differences of cubes, such as 8x³ − 1, 27x³ + 8, and 125x³ − 64. Its 10 multiple-choice items require students to identify the cube roots and select both the correct linear factor and matching quadratic factor, building accuracy with signs and coefficients.
First model how to recognize each expression as a³ + b³ or a³ − b³, then identify the cube roots before applying the corresponding factor pattern. Have students explain why a selected binomial and quadratic pair works, and ask them to expand a few choices to verify the factorization before completing the remaining multiple-choice items independently.
Students may use the difference-of-cubes pattern for a sum, reverse the sign in the binomial factor, or copy that sign incorrectly into the quadratic factor. They may also cube the coefficients incorrectly—for example, treating 27x³ as if its cube root were 27x instead of 3x—so check both the extracted cube roots and the signs in the selected factor pair.
Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for all 10 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.
For the multiple-choice factor pairs on this worksheet, use Advanced Settings to adjust font spacing or increase the font size so the algebraic expressions and answer choices are easier to compare. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the factoring practice.
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