Step by step
The question
Question: simplify (3x² + 2x − 1) − (x² − 5x + 4).
Simplify means: write it shorter, with the same value.
1 Open the brackets
A bracket with a plus or nothing in front can just be removed.
A minus in front of a bracket changes the sign of every part inside.
Now we have 3x² + 2x − 1 − x² + 5x − 4.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x² terms go together.
Plain numbers go together.
Each colour is one kind.
We move like terms next to each other.
Each term takes its sign with it.
3x² − x² is 2x².
It is like 3 apples take away 1 apple: that is 2 apples.
2x + 5x is 7x.
−1 − 4 is −5.
So the expression is 2x² + 7x − 5.
3 Check
Let's check.
We pick a number for each letter: x = 2.
We put it into the start.
Now into our answer.
Both give 17.
Same value, so 2x² + 7x − 5 is right!
Let's look back.
First: open the brackets.
Then: group like terms.
Last: check.