Simplify (x + 2)(x + 3) Step by Step

Step by step

The question

Question: simplify (x + 2)(x + 3).

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

(x + 2)(x + 3)

1 Split the first bracket

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

(a + b)(c + d) = a(c + d) + b(c + d)

The parts of the first bracket are x and 2.

Each one takes the whole second bracket.

= x(x + 3) + 2(x + 3)

2 Open the brackets

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

a(b + c) = ab + ac

So we write each part times what is in front.

= x(x) + x(3) + 2(x) + 2(3)

x times x is x².

x times 3 is 3x.

2 times x is 2x.

2 times 3 is 6.

= x² + 3x + 2x + 6

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.

like terms = same letters,

same powers

3x + 2x is 5x.

It is like 3 apples plus 2 apples: that is 5 apples.

3x + 2x = 5x

So the expression is x² + 5x + 6.

= x² + 5x + 6

4 Check

Let's check.

We pick a number for each letter: x = 2.

We put it into the start.

Start: (2 + 2)(2 + 3) = (4)(5) = 20

Now into our answer.

Answer: 2² + 5 × 2 + 6 = 4 + 10 + 6 = 20

Both give 20.

Same value, so x² + 5x + 6 is right!

Both give 20

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer