An expression is built from terms, separated by plus and minus signs. In 5x² − 3x + 7 there are three: 5x², −3x and 7. The sign belongs to the term after it.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Priya writes 5(x + 2) + 3x as 8x + 2. Sam says something went missing. Rewrite 5(x + 2) + 3x with no brackets and as few terms as possible.
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Coefficient, variable, constant
The number multiplying a letter is its coefficient: 5 in 5x², −3 in −3x. The letter is the variable, and the small 2 is its exponent. A term with no letter, like 7, is a constant. Inside 5x² the factors are 5, x and x, multiplied together.
Like terms
Two terms are like terms when they have the same letter to the same power. 5x and 3x are like terms, and 5x + 3x = 8x: five of something plus three of the same thing is eight of it. 5x and 3x² are not, because x and x² are different quantities, so 5x + 3x² stays exactly as it is.
Distributing
A number outside a bracket multiplies every term inside it. 3(2x + 5) means three lots of 2x + 5: 3 × 2x + 3 × 5 = 6x + 15. Writing 6x + 5 leaves two of the three fives behind. Test it with x = 1: 3(2 + 5) = 21 and 6 + 15 = 21, but 6 + 5 = 11.
Read it backwards and it is factoring
6x + 15 = 3(2x + 5), read from right to left, takes out the 3 that both terms share. Distributing and factoring are one equation read in two directions. To factor 12x + 18, find what both terms share, 6, and write 6(2x + 3). Distribute to check.
Read the structure first
x² − 9 is x² − 3², a difference of two squares, so it factors as (x − 3)(x + 3). 3(x + 2)² − 5 is a subtraction; the thing being subtracted from is three times a square; inside the square is x + 2. Seeing the layers tells you which operation to undo first.
Rewriting never changes the value
Every legal move, combining like terms, distributing, factoring, gives an expression with the same value for every x. So substitute a number to check. 4(2x − 3) + 5x at x = 2 is 4 × 1 + 10 = 14, and 13x − 12 at x = 2 is 26 − 12 = 14. A different result means an illegal step.
Step 2: Try It Yourself
Tap and try it out.
Simplify 4(2x − 3) + 5x
- 14(2x − 3) + 5xthe expression as given
Step 0 of 3
3(2x + 5) = 6x + 15
3 rows of 2x + 5. Gather the bars: 6 x tiles. Gather the squares: 15 units. A bar and a square never combine, because nobody knows how long x is.
Step 3: In Real Life
On a phone bill
A phone plan costs $20 a month plus 5 cents a text: 20 + 0.05t. Reading the structure tells you what changes the bill (the texts) and what never does (the 20). Every bill, wage slip and recipe that scales is an expression, and reading its parts is how you see what you control.
Step 4: Watch an Example
One step at a time.
Watch Noor Simplify 6(x + 2) + 3(2x − 1)
Two brackets, then the answer read backwards, then a check.
- Step 1
The first bracket has a 6 outside it, and the 6 reaches both terms inside: 6 × x = 6x and 6 × 2 = 12. The expression is now 6x + 12 + 3(2x − 1).
Watch Ravi Simplify 4(3x − 2) − 5(x − 3)
The same moves as Noor. The last two steps wait for your answer first.
- Step 1
The 4 reaches both terms in the first bracket: 4 × 3x = 12x and 4 × (−2) = −8. So far the expression is 12x − 8 − 5(x − 3).
Step 5: Your Turn
Practice makes it stick.
The Class Trip
Problem 1 of 2
A trip costs $9 per student for the bus and $4 per student for lunch, plus $30 for the guide. Write the total bill for s students with as few terms as possible.
Four Tickets
Problem 2 of 2
Four friends each pay t dollars for a ticket and $6 for the bus. Write what the group pays, without brackets.
Rewrite and Check
Rewrite each one, then substitute a number to be sure the value did not change.
1 of 5
Expand 3(x + 7).
2 of 5
Combine the like terms in 9x + 4 − 2x + 5.
3 of 5
Combine the like terms in 4x² + 3x − x² + 5x.
4 of 5
Simplify −2(3x − 4) + 7.
5 of 5
Factor 9x + 15 by taking out the largest number both terms share.
Whose Step?
One line in each piece of working has a slip. Find it, then finish the job properly.
1 of 4
Dev simplifies 4(x + 3) + 2x. Which line has the slip?
Dev simplifies 4(x + 3) + 2x
- 14(x + 3) + 2x
- 24x + 3 + 2x
- 34x + 2x + 3
- 46x + 3
2 of 4
Fix Dev's slip and finish. What is 4(x + 3) + 2x once simplified?
3 of 4
Maya simplifies 5x − 2(x − 3) + 4. Which line has the slip?
Maya simplifies 5x − 2(x − 3) + 4
- 15x − 2(x − 3) + 4
- 25x − 2x + 6 + 4
- 35x − 2x + 10
- 47x + 10
4 of 4
Fix Maya's slip and finish. What is 5x − 2(x − 3) + 4 once simplified?
Pick the Move
Nothing to work out. Choose the move, or the form, that fits.
1 of 2
To simplify 3(2x − 5) + 4(x + 1), which move comes first?
2 of 2
All four expressions are equal. Which one has 6 written outside the bracket, with no factor left to take out from inside?
Same Thing?
No expanding needed. Read the structure and decide.
1 of 2
Select every expression equal to 3(x + 4) for every value of x.
2 of 2
Select every expression equal to 6x + 9 for every value of x.
Step 6: Quick Check
Show what you know.
Question 1 of 2
3(4x − 2) expands to 12x − what?
Question 2 of 2
What makes two terms like terms?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Find the number k that makes 3(2x + k) + 4x equal to 10x + 21 for every value of x.
Stretch 2 of 2
Use each of 2, 4 and 7 exactly once as a, b and c in a(bx + c), so that it expands to an expression with x coefficient 8 and constant 28. Write the factored expression.
What You Learned
- Terms are separated by plus and minus signs, and the sign belongs to the term after it.
- Only like terms combine: the same letter to the same power.
- Distributing multiplies everything inside the bracket; factoring is the same equation read backwards.
- Substitute a number to check that a rewrite kept the value.
For the grown-up
The misconception this lesson targets: that a number outside a bracket multiplies only the first term inside it, so 3(x + 4) becomes 3x + 4. Its close cousin is merging unlike terms, 3x + 4 into 7x. One habit catches both: substitute a number into the original and the rewrite, and refuse any rewrite that changes the value.
Why one form beats another — Factored form reveals roots; expanded form is easy to add; vertex form shows a parabola's turning point. There is no single "simplest" form — there is the form that answers your question. Choosing it deliberately is the skill Algebra 1 is really teaching.