Algebra
Grade 3-5Expanding Single Brackets
Expanding a bracket means multiplying everything inside it by whatever is outside, and getting this right, including the signs, underpins almost every later algebra topic. This lesson covers expanding a bracket with a positive number outside, expanding with a negative number outside, expanding with a letter outside, and expanding and simplifying two brackets together.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Expanding with a positive number outside
Multiply each term inside the bracket by the number outside, keeping the sign of each term the same.
5(x + 3) means multiplying both x and 3 by 5, giving 5x + 15.
Expanding with a negative number outside
Multiply each term inside the bracket by the negative number, remembering that multiplying by a negative flips the sign of each term.
−3(x − 4) means multiplying both x and −4 by −3. This gives −3x, and −3 × −4 = 12, so the answer is −3x + 12.
Expanding with a letter outside
Multiply each term inside the bracket by the letter outside. Multiplying the letter by itself gives a squared term.
x(x + 5) means multiplying both x and 5 by x. This gives x × x = x² and x × 5 = 5x, so the answer is x² + 5x.
Expanding and simplifying two brackets
Expand each bracket separately first, being careful with any negative signs, then collect the like terms together.
4(x + 3) + 2(x − 5) expands to 4x + 12 + 2x − 10. Collecting like terms gives 6x + 2.
Worked Examples
Three exam-style questions, fully solved.
Expand 5(x + 3).
Easy- 1.Multiply x by 5: 5 × x = 5x
- 2.Multiply 3 by 5: 5 × 3 = 15
Answer: 5x + 15
Expand −3(x − 4).
Medium- 1.Multiply x by −3: −3 × x = −3x
- 2.Multiply −4 by −3: −3 × −4 = 12
Answer: −3x + 12
Expand and simplify 4(x + 3) + 2(x − 5).
Hard- 1.Expand the first bracket: 4(x + 3) = 4x + 12
- 2.Expand the second bracket: 2(x − 5) = 2x − 10
- 3.Collect like terms: 4x + 12 + 2x − 10 = 6x + 2
Answer: 6x + 2
Avoid These
The most common mistakes students make.
Forgetting to multiply every term inside the bracket by the number outside, especially the second term.
Getting the sign wrong when the number outside the bracket is negative, especially when the term inside is also negative, since two negatives multiply to give a positive.
When a letter is outside the bracket, writing the result of multiplying the letter by itself as just the letter again, instead of as a squared term.
When expanding two brackets and simplifying, only expanding one of the brackets or collecting the like terms before both brackets have been fully expanded.
Losing track of a negative sign when subtracting a whole bracket, since it changes the sign of every term inside that bracket, not just the first one.
FAQ
Questions parents and students ask.
Before this topic, make sure you know
What to learn next
Want a plan built around your child specifically?
Get our free 8-video course, or book a free Roadmap Call for a personalised plan.