A number outside a bracket multiplies every term inside it: 3(x + 4) = 3x + 12.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Every term, without exception
Writing 3x + 4 leaves two of the three lots of 4 behind. Test it with x = 1 and the two forms disagree.
Like terms
Terms combine only when the letter part matches exactly. 5x and 2x combine; 5x and 2x² do not.
Simplify first
Expanding and collecting before solving turns a messy equation into a short one.
Distribute first, then collect
For 3(x + 4) − 2x, expand to 3x + 12 − 2x, then collect to x + 12. Trying to collect across a bracket before expanding is the standard error, because the terms inside are not yet free to combine with those outside.
The sign in front of a bracket
−(x − 3) is −x + 3, not −x − 3. A minus in front means multiplying by −1, which flips every sign inside. Rewriting the minus as × (−1) explicitly, once, is how most people stop making this mistake.
What counts as like terms
3x and 5x are like; 3x and 5x² are not; 3x and 5xy are not. Like terms need identical variable parts, exponents included. Collecting unlike terms is the other half of the errors in this topic.
Substitute to verify
Put x = 2 into both 3(x + 4) − 2x and x + 12: both give 14. Use a value other than 0 or 1, since those can hide sign and coefficient errors. One substitution catches almost everything.
Step 2: Try It Yourself
The bracket drawn as a rectangle, cut into the two products it makes.
7 + 7 + 7 = 21
3 × 7 = 21
3 × 7 = (3 × 4) + (3 × 3) = 12 + 9 = 21
The array is cut into 3 × 4 and 3 × 3. Two easier facts that add to the same total.
Step 3: Watch an Example
One step at a time.
Watch Dev Simplify Before Solving
Dev simplifies 2(x + 3) + 4x.
- Step 1
He expands the bracket: 2x + 6.
Step 4: Your Turn
Practice makes it stick.
The Bracket
Problem 1 of 2
Expand 5(x + 3). What is the number term?
Collecting
Problem 2 of 2
Simplify 7x + 2x. How many x?
Expand and Collect
1 of 8
Expand 4(x + 2). Number term?
2 of 8
Simplify 3x + 5x. How many x?
3 of 8
Expand 6(x − 3). Number term?
4 of 8
Simplify 2(x + 1) + 3x. How many x?
5 of 8
Select every pair that can be combined into one term.
6 of 8
Simplify 2(x + 1) + 3x. What is the number term?
7 of 8
Is 3(x + 4) the same as 3x + 4? 1 for yes, 0 for no.
8 of 8
Order the steps for simplifying 5(x + 2) + 3x.
- 1Collect the x terms
- 2Collect the plain numbers
- 3Expand the bracket
Step 5: Quick Check
Show what you know.
Question 1 of 1
Simplify 3(x + 2) + 4x. How many x?
What You Learned
- A multiplier outside a bracket reaches every term inside it.
- Terms combine only when their letter parts match exactly.
- Expanding and collecting first makes the equation that follows much shorter.