Expand and simplify (x + 3)(x + 5).

Step by step

The question

Question: simplify (x + 3)(x + 5).

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

1 Split the first bracket

Each part of the first bracket multiplies the whole second bracket.

The parts of the first bracket are x and 3.

Each one takes the whole second bracket.

2 Open the brackets

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

So we write each part times what is in front.

x times x is x²: x squared.

x times 5 is 5x.

3 times x is 3x.

3 times 5 is 15.

3 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x terms go together.

Each colour is one kind.

5x + 3x is 8x.

So the expression is x² + 8x + 15.

4 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 35.

Same value, so x² + 8x + 15 is right!

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.