Factoring sums and differences of cubes. Game on.

Factoring sums and differences of cubes is a grade 9 math skill aligned to Common Core standard HSA.APR.C.4. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 factoring sums and differences of cubes problems our math games drill.

CCSS HSA.APR.C.410 questions in the bank
Kickoff

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Warm-upeasy

Which expression is equivalent to x3−27?x^{3} - 27\textsf{?}

x3−27=x3−33=(x−3)(x2+3x+9).x^{3} - 27 = x^{3} - 3^{3} = (x - 3)(x^{2} + 3x + 9)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x3+27?x^{3} + 27\textsf{?}

x3+27=x3+33=(x+3)(x2−3x+9).x^{3} + 27 = x^{3} + 3^{3} = (x + 3)(x^{2} - 3x + 9)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x3−125?x^{3} - 125\textsf{?}

x3−125=x3−53=(x−5)(x2+5x+25).x^{3} - 125 = x^{3} - 5^{3} = (x - 5)(x^{2} + 5x + 25)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x3+8?x^{3} + 8\textsf{?}

x3+8=x3+23=(x+2)(x2−2x+4).x^{3} + 8 = x^{3} + 2^{3} = (x + 2)(x^{2} - 2x + 4)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x3−64?x^{3} - 64\textsf{?}

x3−64=x3−43=(x−4)(x2+4x+16).x^{3} - 64 = x^{3} - 4^{3} = (x - 4)(x^{2} + 4x + 16)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x3+64?x^{3} + 64\textsf{?}

x3+64=x3+43=(x+4)(x2−4x+16).x^{3} + 64 = x^{3} + 4^{3} = (x + 4)(x^{2} - 4x + 16)\textsf{.}

Mid-gameeasy

Which expression is equivalent to x3+125?x^{3} + 125\textsf{?}

x3+125=x3+53=(x+5)(x2−5x+25).x^{3} + 125 = x^{3} + 5^{3} = (x + 5)(x^{2} - 5x + 25)\textsf{.}

Buzzer beatereasy

Which expression is equivalent to 8x3+27?8x^{3} + 27\textsf{?}

8x3+27=(2x)3+33=(2x+3)(4x2−6x+9).8x^{3} + 27 = (2x)^{3} + 3^{3} = (2x + 3)(4x^{2} - 6x + 9)\textsf{.}

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover factoring sums and differences of cubes:
ACTPARCCPSAT/NMSQTDC CAPEGeorgia Milestones
Reporting domains for this skill
ACT All grades: Preparing for Higher MathDC CAPE Algebra I: Arithmetic with Polynomials and Rational ExpressionsDC CAPE Algebra II: Polynomial, Rational, and Radical RelationshipsGeorgia Milestones Algebra I: Arithmetic with Polynomials and Rational ExpressionsGeorgia Milestones Algebra II: Arithmetic with Polynomials and Rational ExpressionsMAAP High School Courses: Algebra I/Integrated Algebra domains
More Grade 9 skills
Factoring quadraticsFraction bounds extreme value (ACT)Factoring patternsFunction table composition (ACT)Factored polynomial x-intercepts (SAT)Geometric sequence equationsFactorable polynomial zeros (ACT)Factoring quadratic expressions (ACT)All Grade 9 practice →

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