Expanding Single Brackets
Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers
What a learner can do afterwards
- Multiply a single positive term over a bracket to expand the expression
- Multiply a negative term over a bracket, correctly handling signs
- Combine expanding brackets with collecting like terms to simplify fully
1 · Read
A bracket like (2x + 5) is a group of terms stuck together. When a number sits right outside the bracket, like in 3(2x + 5), that number multiplies every single term inside. This is called expanding the bracket.
Take 3(2x + 5). Multiply 3 by 2x first: 3 times 2x is 6x. Then multiply 3 by 5: 3 times 5 is 15. Join the results: 3(2x + 5) = 6x + 15.
Now try -2(x - 4). Multiply -2 by x: -2 times x is -2x. Multiply -2 by -4: -2 times -4 is 8, because a negative times a negative is positive. So -2(x - 4) = -2x + 8.
Sometimes you expand first, then tidy up. For 5(x + 2) - 3x, expand to get 5x + 10 - 3x. Then collect the x terms: 5x - 3x = 2x. The simplified answer is 2x + 10.
Picture an arrow running from the outside number to every term inside the bracket. Two terms inside means two multiplications. Skip one, and your answer will be wrong.
Multiply the outside number by every term inside the bracket, keep track of the signs, then collect like terms if you can.
Readings 'Visit every term', 'A negative number outside', 'An area picture of expanding' and 'Expand, then collect' are original to this dataset. All 10 extra questions are original to this dataset.
2 · Watch
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Where it sits
Where this leads
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.