Step by step
The question
Question: find f(a + 1) for f(x) = x² + 2x.
f(x) is read "f of x".
It is a rule, called a function.
A number goes in for x.
The rule gives one answer out.
1 Put the bracket in
f(a + 1) means: put a + 1 in place of every x.
We write (a + 1) in brackets.
It goes in as one piece.
2 Write the square out
A square means the bracket times itself.
(a + 1)² is a + 1 times a + 1.
Careful!
We can't just square each part.
a² + 1 is wrong.
The middle part is missing.
So we write the bracket two times.
3 Split the first bracket
Each part of the first bracket multiplies the whole second bracket.
The parts of the first bracket are a and 1.
Each one takes the whole second bracket.
4 Open the brackets
What is in front of a bracket multiplies every part inside.
So we write each part times what is in front.
a times a is a².
a times 1 is a.
1 times a is a.
1 times 1 is 1.
5 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.
Plain numbers go together.
Each colour is one kind.
We move like terms next to each other.
Each term takes its sign with it.
a + a + 2a is 4a.
1 + 2 is 3.
So the expression is a² + 4a + 3.
6 Check
Let's check.
We pick a number for each letter: a = 2.
We put it into the start.
Now into our answer.
Both give 15.
Same value, so a² + 4a + 3 is right!
Let's look back.
First: put the bracket in.
Then: write the square out.
Then: split the first bracket.
Then: open the brackets.
Then: group like terms.
Last: check.