Expand and simplify single brackets #1
Mastering this skill is essential for fields like computer science and engineering, where complex formulas must be simplified to make software run faster. It is the mathematical equivalent of unpacking multiple boxes of mixed items to see exactly how much total stock you have on the shelves. Jump to the questions
Practise now
Expand and simplify the following expressions:
Topic guide
What this worksheet practises
This worksheet focuses on expanding single brackets and then simplifying the resulting algebraic expression. Expanding brackets is a core algebraic skill required before you can solve complex equations or manipulate formulas.
Key method
To expand a bracket, you must multiply the term immediately outside the bracket by every individual term inside the bracket.
- Draw an arrow from the outside term to the first inside term. Multiply them together.
- Draw a second arrow from the outside term to the second inside term. Multiply them together. Pay close attention to negative signs.
- Write out the newly expanded terms in a line.
- Finally, "simplify" by collecting any like terms together (e.g., adding all the 'x's together and adding all the normal numbers together).
Worked example
Expand and simplify: 3(2x + 4) + 5(x − 2).
Step 1: Expand the first bracket.
Multiply 3 by 2x = 6x.
Multiply 3 by +4 = +12.
This gives: 6x + 12.
Step 2: Expand the second bracket.
Multiply 5 by x = +5x.
Multiply 5 by −2 = −10.
This gives: +5x − 10.
Step 3: Write out the full expanded expression.
6x + 12 + 5x − 10
Step 4: Simplify by collecting like terms. (6x + 5x = 11x, and 12 − 10 = 2).
The final answer is 11x + 2.
Common mistakes to avoid
The most frequent error is only multiplying the outside number by the first thing inside the bracket. For instance, expanding 3(2x + 4) as 6x + 4. You must multiply the 3 by the 4 as well. Drawing physical arrows helps prevent you from forgetting the second term.
How to check your answer
You can check your algebra by substituting a simple number, like x = 2, into both the original question and your final answer. If they are truly equal, the numerical result will be identical.