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

Step by step

The question

Question: simplify (x + 3)(x − 2).

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

(x + 3)(x − 2)

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 3.

Each one takes the whole second bracket.

= x(x − 2) + 3(x − 2)

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(−2) + 3(x) + 3(−2)

− × + = −

Watch the signs.

x times x is x².

x times (−2) is −2x.

3 times x is 3x.

3 times (−2) is −6.

= x² − 2x + 3x − 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

−2x + 3x is x.

−2x + 3x = x

So the expression is x² + x − 6.

= x² + x − 6

4 Check

Let's check.

We pick a number for each letter: x = 3.

We put it into the start.

Start: (3 + 3)(3 − 2) = (6)(1) = 6

Now into our answer.

Answer: 3² + 3 − 6 = 9 + 3 − 6 = 6

Both give 6.

Same value, so x² + x − 6 is right!

Both give 6

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer