Part 02 · Algebra basics · Card 3 of 8
Expanding brackets
Multiplying everything inside the brackets by the number or letter outside.
Last updated
Analogy
Like handing out a gift to every guest at a table, not just the first one.
Example
3(x + 4)
3 x x = 3x3 x 4 = 12So 3(x + 4) = 3x + 12
In practice
A gym charges 3 pounds per class plus 4 pounds booking: 3(x + 4) means each class costs 3 times (x + 4).
Practice
Flashcards
- Expand 3(x + 4).3x + 12. Multiply both terms by 3.
Questions people ask
Do you multiply the number by everything inside the bracket?
Yes. Every term inside gets multiplied, not just the first one. In 5(2x - 3), the 5 multiplies 2x to give 10x and also multiplies -3 to give -15. The answer is 10x - 15. Check with x = 1: 5(2 - 3) = -5 and 10 - 15 = -5.
What if there is a minus sign in front of the bracket?
A minus outside flips the sign of every term inside. So -(x + 4) becomes -x - 4, and -2(x - 3) becomes -2x + 6. Forgetting to flip the second term is the most common mistake. Think of the minus as multiplying by -1.