Brackets under the magnifier – algebraic expressions in two steps
Each task has two steps for one expression: its value for a given number, then the same expression with the bracket multiplied out. After every answer you see the right method next to a typical mistake.
How do you play?
Each task has two steps for the same expression, for example 3(2a − 5). In step 1 you work out its value for a given number and choose one of four answers. In step 2 you choose the expression that equals the one from step 1 after you multiply out the bracket and add like terms. After every answer you see the right method next to the typical mistake behind one of the other answers. There are 5 tasks. At the end you will see where to find the lesson and the worksheet. By default there is no time limit; the timed mode is optional and only counts the time while a question is waiting for your answer.
How do you multiply out a bracket?
Multiply the number in front of the bracket by every term inside it, together with its sign. 3(2a − 5): 3 · 2a = 6a and 3 · (−5) = −15, so 3(2a − 5) = 6a − 15. When there is a minus in front of the bracket, you multiply by −1, so every term changes its sign: −3(2a − 5) = −6a + 15.
Then add like terms: terms with the same letter, or plain numbers. 4a + 6a = 10a and 7 − 15 = −8. A term with a letter and a plain number are not like terms, so they cannot be added into one term.
How do you substitute a negative number?
Put a negative number in brackets so that you do not lose the minus. For a = −3 the expression 2a − 5 is 2 · (−3) − 5 = −6 − 5 = −11. Work out the bracket first, then the multiplication in front of the bracket, and the rest of the expression last.
What is the most common mistake?
Multiplying only the first term of the bracket: 3(2a − 5) = 6a − 5. A check for a = 4 shows it: 3(2a − 5) gives 9, but 6a − 5 gives 19. Another common mistake is a lost minus: −3(2a − 5) = −6a − 15 instead of −6a + 15, because a minus in front of the bracket changes the sign of every term, not just the first one.
How does this help in the eighth-grade exam?
In the Polish eighth-grade exam in 2026, question 8 asked pupils to work out the value of an algebraic expression and then rewrite it as an algebraic sum. 43% of pupils solved it correctly, and it was the hardest of the questions that test the third general requirement. 63% of pupils worked out the value correctly, and 59% multiplied out the bracket correctly.
Source: CKE report 2026, p. 42 (in Polish). Curriculum: algebraic expressions, grades 7–8 (Polish core curriculum, Dz.U. 2024 poz. 996).
Mini glossary: English – Polish
- algebraic expression – wyrażenie algebraiczne
- bracket – nawias
- algebraic sum – suma algebraiczna
- like terms – wyrazy podobne
- value of an expression – wartość wyrażenia
The game runs in your browser. There is a time limit only in the timed mode, there are no negative points and we save nothing.