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

Step by step

The question

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

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

1 Open the brackets

The (−4) in front of the bracket multiplies every part inside.

So we write (−4) times each part.

Watch the signs.

(−4) times a is −4a.

(−4) times (−b) is 4b.

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.

Each colour is one kind.

We move like terms next to each other.

Each term takes its sign with it.

3a − 4a is −a.

It is like 3 apples take away 4 apples: that is 1 apple.

2b + 4b is 6b.

So the expression is −a + 6b.

3 Check

Let's check.

We pick a number for each letter: a = 2, b = 3.

We put it into the start.

Now into our answer.

Both give 16.

Same value, so −a + 6b is right!

Let's look back.

First: open the brackets.

Then: group like terms.

Last: check.