wunder beta✖️ The Distributive Property
Multiply a term across parentheses so 3(2x + 5) becomes 6x + 15, and learn to handle negative multipliers without flipping the wrong signs.
What you’ll learn
- Expanding Single BracketsExpand a single term over a bracket using the distributive property, including expressions with negative multipliers, handling signs correctly.The distributive property means the term outside a bracket multiplies every term inside: a(b + c) = ab + ac. So 3(2x + 5) = 6x + 15. It works because a number like 24 can be split (3 × 24 = 3 × 20 + 3 × 4 = 72). A negative multiplier carries its sign to each term: −2(x − 4) = −2x + 8, since negative times negative is positive. The common error is multiplying only the first term — always multiply them all.
Questions this course answers
What does the distributive property tell you to do with a(b + c)?
The multiplier reaches every term: a(b + c) = ab + ac.
Expand −2(x − 4).
−2 × x = −2x and −2 × (−4) = +8, so −2x + 8.
Which expansion of 5(x + 3) is correct?
Both terms are multiplied: 5 × x = 5x and 5 × 3 = 15.
Why is 3 × 24 the same as 3 × 20 + 3 × 4?
Distribution shares the multiplier across each part: 60 + 12 = 72.
Expand 2(3x − 1).
2 × 3x = 6x and 2 × (−1) = −2, so 6x − 2.
Grounded in trusted sources
- BBC Bitesize — Maths (Key Stage 3)
- Khan Academy — Distributive property
- NRICH (University of Cambridge)
- Britannica
Every Wunder lesson is built from real, reputable sources — never invented.
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