Step by step
The question
Question: simplify (3x² + 2x − 1) − (x² − 4x + 5).
Simplify means: write it shorter, with the same value.
There are four choices.
First we solve it, the normal way.
Then we pick.
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.
It is like −1 times the bracket.
+x² becomes −x².
−4x becomes +4x.
+5 becomes −5.
Now we have 3x² + 2x − 1 − x² + 4x − 5.
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.
x² alone means 1x².
3x² − x² is 2x².
It is like 3 apples take away 1 apple: that is 2 apples.
2x + 4x is 6x.
−1 − 5 is −6.
So the expression is 2x² + 6x − 6.
3 Check
Let's check.
We pick a small number for each letter: x = 2.
Any number works, and a small one keeps the sums easy.
We put it into the question.
Now into our answer.
Both give 14.
Same value, so 2x² + 6x − 6 is right!
4 Pick the choice
Our answer is 2x² + 6x − 6.
That is choice B.
5 Why not the others
A is 2x² − 2x + 4.
Wrong: forgot to change the signs: −(−4x) is +4x.
C is 2x² + 6x + 4.
Wrong: −1 − 5 is −6, not +4.
D is 4x² − 2x + 4.
Wrong: added the brackets: 3x² + x².
Let's look back.
First: open the brackets.
Then: group like terms.
Then: check.
Then: pick the choice.
Last: why not the others.