8 questions
9th - 9th Grade
Mathematics
Multiplying Polynomials is a Grade 9 mathematics worksheet that gives students eight multiple-choice problems involving polynomial multiplication. Students expand binomials such as (x + 2)(x + 3), multiply a binomial by a trinomial, distribute a monomial across a polynomial, and use special products such as a square of a binomial and a difference of squares. The final item applies polynomial multiplication to finding the area of a rectangle with algebraic dimensions. The questions require students to distribute each term, combine like terms, track coefficients and exponents, and recognize equivalent polynomial forms. The worksheet provides varied practice with expressions from linear through cubic products, including sign-sensitive examples such as (x + 10)(x − 10). It is designed for Grade 9 math instruction, independent practice, review, or a quick check of procedural fluency. This free printable worksheet includes a complete answer key for efficient checking.
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WorksheetsAnswer KeyThis Grade 9 worksheet contains eight multiple-choice questions on expanding and simplifying polynomial products. Students multiply binomials and binomials by trinomials, distribute a monomial, apply the square of a binomial and difference-of-squares patterns, and use polynomial multiplication to find the area of a rectangle with algebraic dimensions.
Model one product by showing how every term in the first factor is multiplied by every term in the second, then combine like terms before students work independently. Use the questions involving (x + 5)² and (x + 10)(x − 10) to connect distribution with special-product patterns, and ask students to explain how the rectangle-area problem represents the same multiplication process.
Check whether students multiply every term rather than only the first terms, especially in the binomial-by-trinomial problems. Common errors include misadding exponents, losing negative signs in expressions such as (x − 10), failing to combine like terms, and using x² + 25 instead of x² + 10x + 25 for (x + 5)².
The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all eight multiple-choice questions. You can grade printable student work by scanning it with the Wayground for Teachers app, or review responses through the digital quiz.
The worksheet progresses across several product types: binomial-by-binomial multiplication, binomial-by-trinomial multiplication, monomial distribution, a squared binomial, and a difference of squares. It also includes an application item in which students expand (x − 5)(3x + 1) to determine a rectangle’s area expression.
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