Simplify 4(a + 2) + 3(a - 1)

Step by step

The question

Question: simplify 4(a + 2) + 3(a − 1).

Simplify means: write it shorter, with the same value.

1 Open the brackets

What is in front of a bracket multiplies every part inside.

So we write each part times what is in front.

Watch the signs.

4 times a is 4a.

4 times 2 is 8.

3 times a is 3a.

3 times (−1) is −3.

2 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.

4a + 3a is 7a.

It is like 4 apples plus 3 apples: that is 7 apples.

8 − 3 is 5.

So the expression is 7a + 5.

3 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 19.

Same value, so 7a + 5 is right!

Let's look back.

First: open the brackets.

Then: group like terms.

Last: check.