Multiplying Polynomials

Algebra Foundation

Algebra 1

Study expressions, equations, inequalities, functions, linear models, systems, polynomials, quadratics, and exponential growth with original explanations and worked examples.

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Algebra 1 · Unit 7 · Topic 7.4

Multiplying Polynomials

Polynomial multiplication distributes each term of one factor to every term of the other.

Definition and explanation

Polynomial multiplication distributes each term of one factor to every term of the other. Combine like terms after computing all products.

Worked example

Expand (2x − 3)(x + 4). The four products are 2x², 8x, −3x, and −12, so the result is 2x² + 5x − 12. At x = 1, both forms equal −5.

Common mistake

Multiplying only the first and last terms misses the cross terms.

Key takeaway

Polynomial multiplication distributes each term of one factor to every term of the other.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.