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
The lesson
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 x 2x = 6x. Then multiply 3 by 5: 3 x 5 = 15. Join the results: 3(2x + 5) = 6x + 15.
Now try -2(x - 4). Multiply -2 by x: -2 x x = -2x. Multiply -2 by -4: -2 x -4 = 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.
Watch it
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.