To expand 3(x + 4), multiply everything inside the bracket by the number outside. 3 × x = 3x and 3 × 4 = 12, so 3(x + 4) = 3x + 12.
Watch the signs: 2(4x − 5) = 8x − 10. This uses the distributive property, which also works with numbers: 6 × 23 = 6 × 20 + 6 × 3. Expanding and then collecting like terms lets you simplify longer expressions.
Worked example
Expand and simplify 2(3x + 1) + 4x
- Expand: 2(3x + 1) = 6x + 2.
- Collect like terms: 6x + 4x = 10x.
Answer:10x + 2
Key words
- expand
- multiply out the brackets
- distributive property
- a(b + c) = ab + ac
- bracket
- groups terms together
Practise this
New questions every time.
Common Core-referenced: 6.EE.A.3