Expand an expression using distributivity

The distributive law

To expand an expression of the form k(a+b), we multiply k by each term inside the brackets, then add them together:

k × (a + b) = k × a + k × b

Example: 4(x + 3) = 4 × x + 4 × 3 = 4x + 12

The same applies to subtraction: k × (a – b) = k × a – k × b

Example: 5(x – 2) = 5x – 10

Detailed examples

Expression to expand	Step	Result
3(x + 4)	3x × x + 3x × 4	3x + 12
2(x - 5)	2x × x - 2x × 5	2x - 10
-3(x + 2)	-3xx + (-3)x2	-3x - 6

Expand and then simplify

Often, after expanding, you still need to simplify the resulting expression.

Example: J = 2(x + 3) + 4x Step 1 (expand): J = 2x + 6 + 4x Step 2 (simplify): J = (2x + 4x) + 6 = 6x + 6

Common pitfall

Watch out for the sign in front of a set of brackets! When the number in front is negative, you must multiply each term by that negative number, including its sign. Thus, -3(x + 2) = -3x - 6, not -3x + 6. A very common mistake is to forget to distribute the negative sign to the second term.