A number outside a bracket multiplies every term inside it. 3(x + 4) is three lots of x + 4: 3 × x + 3 × 4 = 3x + 12.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Which of these equals 2(3x − 5)? Test each with x = 4.
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Every term, without exception
Writing 3x + 4 leaves two of the three fours behind. Test it with x = 1: 3(1 + 4) = 15, and 3 + 12 = 15, but 3 + 4 = 7. A substitution catches a half-distributed bracket every time.
A negative outside
−2(x − 5) multiplies both terms by −2: −2x + 10. The minus outside meets the minus inside, and the second term turns positive. Losing that sign is the commonest slip, so write both products before you tidy.
Like terms
Terms combine only when the letter part matches exactly. 5x + 2x = 7x: five of a thing and two more of it. 5x + 2x² stays as it is, because x and x² are different quantities.
Collect after expanding
2(x + 3) + 4x: expand to 2x + 6 + 4x, then gather. 2x + 4x = 6x, and the 6 has no partner: 6x + 6. Expand first, collect second, each move on its own line.
Simplify before solving
The equation 2(x + 3) + 4x = 30 is 6x + 6 = 30 once simplified: two moves to solve instead of five. Expanding and collecting first turns a messy equation into a short one.
Check by substituting
Both forms must agree for every value of x. 2(x + 3) + 4x at x = 2 is 10 + 8 = 18; 6x + 6 at x = 2 is 18. Agreement at one value is not a proof, but disagreement is proof of a mistake.
Step 2: Try It Yourself
Tap and try it out.
Simplify 2(x + 3) + 4x
- 12(x + 3) + 4xthe expression as given
Step 0 of 3
3(x + 4) = 3x + 12
3 rows of x + 4. Gather the bars: 3 x tiles. Gather the squares: 12 units. A bar and a square never combine, because nobody knows how long x is.
Step 3: In Real Life
A warehouse invoice
Five packs each holding a pen and 3 pencils, minus 2 pens returned: 5(p + 3q) − 2p = 3p + 15q. Distribute, then collect. An invoice is built from these two moves.
Step 4: Watch an Example
One step at a time.
Watch Ana Simplify 3(2x − 1) − 4(x − 2)
Two brackets. The second is multiplied by −4, and the sign is part of the multiplier.
- Step 1
The 3 reaches both terms in its bracket: 3 × 2x = 6x and 3 × 1 = 3, and the minus between them stays. So far the line reads 6x − 3 − 4(x − 2).
Watch Ravi Simplify 4(2x − 3) − 3(x − 5)
The same kind of expression. Ravi writes the first two lines, and the last two wait for your answer.
- Step 1
Distributing the 4 comes first: 4 × 2x = 8x and 4 × 3 = 12, with the minus kept, so the first bracket becomes 8x − 12. The line reads 8x − 12 − 3(x − 5).
Step 5: Your Turn
Practice makes it stick.
The Garden Bed
Problem 1 of 2
A garden bed is 2x feet long and x + 3 feet wide. Its perimeter is 2(2x) + 2(x + 3). Write the perimeter with the brackets gone and the like terms collected.
The Tickets
Problem 2 of 2
A ticket costs t dollars, and a $3 fee is added to every ticket. Sam buys 5 tickets and then uses a $10 voucher. Write what Sam pays, simplified.
Expand and Collect
1 of 5
Expand 3(x + 5).
2 of 5
Expand 4(x − 6).
3 of 5
Expand −4(x − 3).
4 of 5
Simplify 4(x + 3) + 2x.
5 of 5
Simplify 7x − 2(x − 3).
Whose Step?
Each page of working has one line that slipped. Find it, then write what the working should have reached.
1 of 6
Priya simplified 5(x + 2) + 3x. One line has a slip. Which line?
Priya's working: simplify 5(x + 2) + 3x
- 15(x + 2) + 3x
- 25x + 2 + 3x
- 38x + 2
2 of 6
Priya fixes the slip. What does 5(x + 2) + 3x simplify to?
3 of 6
Dev simplified 6x − 2(x − 4). One line has a slip. Which line?
Dev's working: simplify 6x − 2(x − 4)
- 16x − 2(x − 4)
- 26x − 2x − 8
- 34x − 8
4 of 6
Dev fixes the slip. What does 6x − 2(x − 4) simplify to?
5 of 6
Leo simplified 2(x² + 4) + 3x. One line has a slip. Which line?
Leo's working: simplify 2(x² + 4) + 3x
- 12(x² + 4) + 3x
- 22x² + 8 + 3x
- 35x² + 8
6 of 6
Leo fixes the slip. What does 2(x² + 4) + 3x simplify to?
Pick the Move
1 of 2
To simplify 4(x − 2) + 3x, which move comes first?
2 of 2
Noor wants to simplify 8 − 3(x − 2). Which first move is right?
Same Thing?
1 of 2
Select every expression equal to 2(x + 3) + 4.
2 of 2
Select every expression equal to 5x − 3(x − 2).
Step 6: Quick Check
Show what you know.
Question 1 of 1
Simplify 3(x + 2) + 4x. How many x?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Find whole numbers a and b so that a(2x + b) + 3x simplifies to 11x + 12. What is b?
Stretch 2 of 2
What expression must be subtracted from 5x to leave 2(x + 4)?
What You Learned
- A multiplier outside a bracket reaches every term inside it, sign included.
- Expand first, then collect, and write each move on its own line.
- Terms combine only when their letter parts match exactly.
- Substitute a number: both forms must agree.
For the grown-up
The misconception this lesson targets: a multiplier outside a bracket that reaches only the first term, and a negative multiplier that keeps its size but drops its sign. Substituting one number into both forms exposes either slip in a line.