Algebra uses letters to represent unknown numbers. Instead of saying "a number plus 3", we write n + 3. Once you know the rules, algebra is like a secret code you can always crack!
📝 Writing Expressions
"5 more than x" → x + 5 | "3 times y" → 3y Letters stand for unknown values
✅ Like Terms — Can Collect
3x + 5x = 8x | 4y − y = 3y Same letter = like terms. Add/subtract the coefficients.
❌ Unlike Terms — Cannot Collect
3x + 2y cannot be simplified 5x + 3x² cannot be simplified Different letters or powers = unlike terms
Key Vocabulary:
TERM
A single part of an expression: 3x, 7, −2y
COEFFICIENT
The number in front of the letter: in 5x, the coefficient is 5
EXPRESSION
A collection of terms: 3x + 2y − 5
LIKE TERMS
Terms with the same letter: 3x and 7x
The Golden Rules:
Rule 1 — Writing: 3 × n is written as 3n. n × n is written as n². n ÷ 4 is written as n/4.
Rule 2 — Like terms: Only collect terms with exactly the same letter (and same power). Add or subtract the coefficients.
Rule 3 — Numbers: Plain numbers (constants) are like terms with each other: 5 + 3 = 8.
Rule 4 — Order: Write the simplified expression with letter terms first, then the number: 5x + 3, not 3 + 5x.
Rule 5 — Invisible 1: Just "x" means 1x. Just "−y" means −1y.
📝 Worked Examples
Follow each step carefully!
Example 1: Writing an Expression
Question: Write an expression for "double a number n, then subtract 4".
Double n → 2n
Then subtract 4 → 2n − 4
Answer: 2n − 4
Example 2: Collecting Like Terms (one variable)
Question: Simplify 5x + 3x − 2x
All terms are x-terms (like terms) ✓
Collect coefficients: 5 + 3 − 2 = 6
Answer: 6x
Example 3: Collecting Like Terms (two variables)
Question: Simplify 4a + 3b + 2a − b
Group a-terms: 4a + 2a = 6a
Group b-terms: 3b − b = 2b (remember: b = 1b)
Answer: 6a + 2b
Example 4: Simplifying with Numbers
Question: Simplify 3x + 5 + 2x − 1
Group x-terms: 3x + 2x = 5x
Group numbers: 5 − 1 = 4
Answer: 5x + 4
🔬 Expression Builder
Enter coefficients to build and simplify an expression with x and y terms!
+
🧩 Drag 1: Spot the Like Terms
From the expression 4x + 3y + 2x + 5, drag the like terms of 4x into the box.
2x
3y
5
Like term of 4x:
🧩 Drag 2: Collect the x Terms
Simplify: 5x + 3x − 2x. Drag the correct answer.
6x
8x
10x
5x + 3x − 2x =
🧩 Drag 3: Two Variables
Simplify: 4a + 3b + 2a − b. Drag the simplified a and b terms.
6a
2b
7a
4b
Answer:+
🧩 Drag 4: With Numbers
Simplify: 3x + 5 + 2x − 1. Drag the x term and the number.
5x
4
6x
6
+
🧩 Drag 5: Write the Expression
Drag the correct expression for: "4 more than triple n"
3n+4
4n+3
n+7
Expression =
🧩 Drag 6: Full Simplify
Simplify: 2x + 4y + 5 + 3x − 2y + 1. Drag all three parts of the answer.
5x
2y
6
4x
3y
5
++
📝 Practice Questions
Write an expression for "5 more than x".
Write an expression for "double y minus 3".
Write an expression for "a number n divided by 4".
Write an expression for "3 less than 4 times p".
Simplify: 6x + 2x
Simplify: 8y − 3y
Simplify: 4a + 7a − 2a
Simplify: 5x + 3 + 2x
Simplify: 9n − 4 − 3n + 1
Simplify: 3a + 2b + 4a
Simplify: 5x + 2y − 3x + y
Simplify: 4m + 3n − m + 2n
Simplify: 2x + 3y + x − 2y + 4
Simplify: 7p − 3q + 2p + 5q − 1
Simplify: 3a + 4b − a − 4b + 2
Write an expression for the perimeter of a rectangle with length (x + 3) and width x.
Can 4x + 3y be simplified further? Explain why or why not.
What is the coefficient of y in the expression 5x − 3y + 2?
Simplify: 6x + 2 − x − 5 + 3x
A bag has n sweets. Tom takes 3 and then adds 2n more. Write an expression for the total.
x + 5
2y − 3
n/4
4p − 3
8x
5y
9a
7x + 3
6n − 3
7a + 2b
2x + 3y
3m + 5n
3x + y + 4
9p + 2q − 1
2a + 2
2(x + 3) + 2x = 4x + 6
No — 4x and 3y are unlike terms (different letters)
−3
8x − 3
n − 3 + 2n = 3n − 3
🔥 Challenge: Algebra Expression Problems
A rectangle has length (3x + 2) cm and width (x + 1) cm. Write and simplify an expression for its perimeter.
Sam has x cards. He buys 4 more packs of 5 cards each, then gives away 3 cards. Write a simplified expression for how many he has.
The angles of a triangle are (2x + 10)°, (3x − 5)° and (x + 15)°. Write a simplified expression for the sum of the angles.
A shop sells pens for p pence and rulers for r pence. Write an expression for buying 3 pens and 2 rulers. If you also get 50p change from £5, write an expression for the cost.
Simplify: 5a + 3b − 2a + 4c + b − c
A square has side length (2n + 1) cm. Write an expression for its perimeter. Simplify fully.
Two expressions are added: (3x + 4y − 2) and (x − 2y + 7). Write the simplified result.
How many terms does the simplified expression 5x + 3y − 2z + 1 have? List them.
A farmer has 3 fields. Field A has (2x + 5) trees, Field B has (x − 1) trees, Field C has (3x + 4) trees. Write a simplified expression for the total number of trees.