Simplify (x - 3)^2 Step by Step

Step by step

The question

Question: simplify (x − 3)².

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

(x − 3)²

1 Write the square out

A square means the bracket times itself.

(x − 3)² is x − 3 times x − 3.

( )² = ( )( )

Careful!

We can't just square each part.

x² + 9 is wrong.

The middle part is missing.

Careful: not (x − 3)² = x² + 9 ✗

So we write the bracket two times.

= (x − 3)(x − 3)

2 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 − 3) − 3(x − 3)

3 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) + (−3)(x) + (−3)(−3)

− × − = +

Watch the signs.

x times x is x².

x times (−3) is −3x.

(−3) times x is −3x.

(−3) times (−3) is 9.

= x² − 3x − 3x + 9

4 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 − 3x is −6x.

−3x − 3x = −6x

So the expression is x² − 6x + 9.

= x² − 6x + 9

5 Check

Let's check.

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

We put it into the start.

Start: (2 − 3)² = (−1)² = 1

Now into our answer.

Answer: 2² − 6 × 2 + 9 = 4 − 12 + 9 = 1

Both give 1.

Same value, so x² − 6x + 9 is right!

Both give 1

Let's look back.

First: write the square out.

Then: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer