What this covers
Distributive property and expanding polynomials is taught in Grade 8 (age 13 to 14) as a topic to introduce. It sits in the Algebra strand.
Worked example
Expand and simplify: 3(2x - 4) + 2(x + 5)
- Expand the first bracket: 3 × 2x - 3 × 4 = 6x - 12
- Expand the second bracket: 2 × x + 2 × 5 = 2x + 10
- Collect like terms: (6x + 2x) + (-12 + 10) = 8x - 2
Answer: 8x - 2
Difficulty scale
The sheet generator offers five difficulty settings for this topic.
- Single bracket with positive integer outside, e.g., 3(x + 4)
- Single bracket with negative multiplier or variable outside, e.g., -2(3x - 5) or x(x + 2)
- Expanding two single brackets and collecting like terms, e.g., 4(x + 3) - 2(x - 1)
- Double brackets of form (x + a)(x + b) with integers
- 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.
- 8.EE.C.7 Solve linear equations in one variable with rational number coefficients, including equations requiring expanding brackets.