3n + 4n is 7n, in the same way that 3 apples and 4 apples are 7 apples.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
What makes terms alike
Terms are alike when the letter part matches exactly. 3n and 4n are alike; 3n and 4 are not.
Unlike terms stay apart
3n + 4 cannot be tidied further. There is no single term that means both.
The value never changes
3n + 4n and 7n give the same answer for every n. That is what equivalent means.
What makes terms alike
Like terms have exactly the same letter part: 3n and 5n are alike, and 3n and 3n² are not. You can add like terms because you are counting the same thing — three ns plus five ns is eight ns, exactly as three apples plus five apples is eight apples.
Unlike terms simply stay
3n + 5 cannot be simplified to 8n or 8. The n and the 5 are different kinds of thing. An expression that cannot be combined further is not unfinished — it is already in its simplest form.
Take the sign with the term
In 7n − 3n + 2n, the signs belong to the terms that follow them: +7n, −3n, +2n, totalling 6n. Losing a minus sign while rearranging is the commonest error here, so move each sign with its term.
Check by substituting
Put n = 2 into 7n − 3n + 2n and into 6n: both give 12. Substituting the same value into the original and the simplified form is a fast, reliable check on any simplification.
Step 2: Try It Yourself
Tap and try it out.
3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
7 × 3 = 21
7 rows of 3 makes 21.
Step 3: Watch an Example
One step at a time.
Watch Ana Tidy an Expression
Ana simplifies 5n + 2 + 3n + 6.
- Step 1
She groups the n terms: 5n and 3n.
Step 4: Your Turn
Practice makes it stick.
The Check
Problem 1 of 2
Simplify 4n + 5n, then evaluate it when n is 3.
The Same Value
Problem 2 of 2
Evaluate 4n + 5n when n is 3, without simplifying first.
Collect the Terms
1 of 4
Simplify 2n + 6n. How many n?
2 of 4
Simplify 9n − 4n. How many n?
3 of 4
Can 3n + 5 be simplified to 8n?
4 of 4
Simplify 3n + 2 + 4n. How many n?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Simplify 6n + 3n. How many n?
What You Learned
- Like terms have exactly the same letter part.
- Add the counts of like terms; leave unlike terms alone.
- Simplifying changes how the expression looks, never what it is worth.