Step by step
The question
Question: simplify 4a + 3b − a + 2b.
Simplify means: write it shorter, with the same value.
4a + 3b − a + 2b
1 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the a terms go together.
Each colour is one kind.
like terms = same letters,
same powers
We move like terms next to each other.
Each term takes its sign with it.
= 4a − a + 3b + 2b
4a − a is 3a.
It is like 4 apples take away 1 apple: that is 3 apples.
3b + 2b is 5b.
4a − a = 3a
3b + 2b = 5b
So the expression is 3a + 5b.
= 3a + 5b
2 Check
Let's check.
We pick a number for each letter: a = 2, b = 3.
We put it into the start.
Start: 4 × 2 + 3 × 3 − 2 + 2 × 3
= 8 + 9 − 2 + 6 = 21
Now into our answer.
Answer: 3 × 2 + 5 × 3 = 6 + 15 = 21
Both give 21.
Same value, so 3a + 5b is right!
Both give 21
Let's look back.
First: group like terms.
Last: check.
Answer
= 3a + 5b