Polynomials
Multiplying monomials worksheets
Simplify products and powers of monomials. Choose from 48 structures, positive or negative exponents and coefficients, and 12, 15 or 18 problems with exact answers.
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Factoring monomials worksheets
Factor ten monomials into primes and variable factors. Choose expression structures, coefficient ranges and repeated factors or prime-power notation, with exact worked answers.
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Factor the numerical coefficient first, then account for every variable factor. Use repeated factors or exponents as requested.
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Customize this worksheetTwo ways to write the same factorization
Repeated-factor notation shows every numerical prime and every copy of a variable. Prime-power notation groups repeated factors with exponents. Both answers must multiply back to the original monomial.
Each customized student worksheet and its answer key use the same generated questions. Start with a focused set of structures, check the worked reasoning, then generate a fresh set when the learner is ready.
Learning objective
What this activity builds
Decompose a monomial into numerical prime factors and variable factors.
Worked example
Write the prime factorization and prime-power factorization of 18x²y.
Repeated factors: 2 × 3 × 3 × x × x × y. Prime powers: 2 × 3² × x² × y.
Both products reconstruct 18x²y. Prime-power notation groups repeated factors without changing their value.
Teaching notes
Make the practice count
- Check the coefficient by multiplying the numerical factors.
- Count each occurrence of every variable.
- Keep repeated-factor and exponent notation distinct.
- Recompose the complete product to verify the answer.
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Choose the expression structures to practice. Answer editions show the steps for each problem.
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Related activities
Polynomials
Identifying polynomial degree worksheets
Find the degree of ten monomials and polynomials. Select one through six terms, compare term degrees and check a separate key with the exponent calculations.
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