Free Printable WorksheetMathAlgebra IIMath CurriculumA-APR.1

ALG2.47 Checking Factoring by Multiplying Back Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.47 Checking Factoring by Multiplying Back. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.47 Checking Factoring by Multiplying Back - Confirm a factorization by expanding the product and matching the original expression term-by-term. Associated source-listed standards: CCSS A-APR.1; MP.6; CA CCSSM A-APR.1; MP.6; MA 2017 A-APR.1; MP.6; NY NGLS A-APR.1; MP.6; TX TEKS Algebra II: §111.40.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG2.47 Checking Factoring by Multiplying Back skill assessments:

Problem 1Difficulty: Mastery
A factorization is checked by expanding it. What do you get from (2p - q)(p + 4q)(p - q)?
A2p3 + 6p2q - 11pq2 + 4q3
B2p3 - 5p2q - 11pq2 + 4q3
C2p3 + 7p2q - 11pq2 + 4q3
D2p3 + 5p2q - 11pq2 + 4q3
Solution & Explanation:Multiply back (2p - q)(p + 4q)(p - q) to get 2p3 + 5p2q - 11pq2 + 4q3. That exact product is the correct choice.
Problem 2Difficulty: Mastery
Use multiplication to verify the statement a3 + 4a2b + ab2 - 6b3 = (a + 3b)(a - b)(a + 2b). Is the statement correct?
ATrue
BFalse
Solution & Explanation:Expanding (a + 3b)(a - b)(a + 2b) gives a3 + 4a2b + ab2 - 6b3. That matches a3 + 4a2b + ab2 - 6b3 term for term, so the claim is correct.
Problem 3Difficulty: Mastery
Multiply back the options. Which factorization correctly verifies y3 + 7y2 - 4y - 28?
A(y + 3)(y - 2)(y + 7)
B(y + 2)(y - 2)(y + 7)
C(y - 2)(y - 2)(y + 7)
D(y + 4)(y - 2)(y + 7)
Solution & Explanation:Multiplying back (y + 2)(y - 2)(y + 7) gives y3 + 7y2 - 4y - 28. The other choices change at least one sign or coefficient.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard A-APR.1 (Confirm a factorization by expanding the product and matching the original expression term-by-term. Associated source-listed standards: CCSS A-APR.1; MP.6; CA CCSSM A-APR.1; MP.6; MA 2017 A-APR.1; MP.6; NY NGLS A-APR.1; MP.6; TX TEKS Algebra II: §111.40.).

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