Polynomials
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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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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Simplify the coefficient, combine matching variable powers and apply any outer exponent to the whole grouped monomial. Observe the stated nonzero-variable conditions.
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Customize this worksheetKeep the expression and its domain together
A negative exponent represents a reciprocal, so its base must be nonzero. Simplifying a product can cancel those exponents without removing the restriction from the original expression. The worked key keeps those conditions visible.
Use a focused selection of expression structures to practice one rule, then combine structures once products, outer powers and coefficient signs are secure.
Learning objective
What this activity builds
Apply product and power rules while preserving signs and nonzero-variable conditions.
Worked example
Simplify (2x⁻²y³)(−3x⁵y⁻¹), where x and y are nonzero.
−6x³y².
Multiply 2 by −3, then add exponents for each variable: −2 + 5 = 3 and 3 + (−1) = 2. The original negative powers still require nonzero x and y.
Teaching notes
Make the practice count
- Treat an outer exponent as applying to the coefficient and every factor.
- Use parentheses to distinguish a negative coefficient from a negative power.
- Retain domain conditions even when powers cancel.
- Check answers with a simple allowed nonzero substitution.
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Multiplying binomials worksheets
Expand ten products of two binomials. Choose among four expression structures, form every term pair and collect like terms with a separate worked key.
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