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

Step by step

The question

Question: simplify (2x − 3)².

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

(2x − 3)²

1 Write the square out

A square means the bracket times itself.

(2x − 3)² is 2x − 3 times 2x − 3.

( )² = ( )( )

Careful!

We can't just square each part.

4x² + 9 is wrong.

The middle part is missing.

Careful: not (2x − 3)² = 4x² + 9 ✗

So we write the bracket two times.

= (2x − 3)(2x − 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 2x and −3.

Each one takes the whole second bracket.

= 2x(2x − 3) − 3(2x − 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.

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

− × − = +

Watch the signs.

2x times 2x is 4x².

2x times (−3) is −6x.

(−3) times 2x is −6x.

(−3) times (−3) is 9.

= 4x² − 6x − 6x + 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

−6x − 6x is −12x.

−6x − 6x = −12x

So the expression is 4x² − 12x + 9.

= 4x² − 12x + 9

5 Check

Let's check.

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

We put it into the start.

Start: (2 × 2 − 3)² = (1)² = 1

Now into our answer.

Answer: 4 × 2² − 12 × 2 + 9 = 16 − 24 + 9

= 1

Both give 1.

Same value, so 4x² − 12x + 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