Distributive property and expanding polynomials: Grade 9 math

What this covers

Distributive property and expanding polynomials is taught in Grade 9 (age 14 to 15) as a main teaching focus. It sits in the Algebra strand.

Worked example

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

1. Single bracket with positive integer outside, e.g., 3(x + 4)
2. Single bracket with negative multiplier or variable outside, e.g., -2(3x - 5) or x(x + 2)
3. Expanding two single brackets and collecting like terms, e.g., 4(x + 3) - 2(x - 1)
4. Double brackets of form (x + a)(x + b) with integers
5. Double brackets with non-unitary x coefficients, e.g., (2x - 3)(3x + 4)

Common mistakes

• Multiplying only the first term inside the bracket by the outside term
• Errors with double negatives, e.g. calculating -3(x - 4) as -3x - 12

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

• Use the structure of an expression to identify ways to rewrite it, such as factoring quadratic and polynomial expressions.