Simplify (2x + 1)^2 Step by Step

Step by step

The question

Question: simplify (2x + 1)².

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

(2x + 1)²

1 Write the square out

A square means the bracket times itself.

(2x + 1)² is 2x + 1 times 2x + 1.

( )² = ( )( )

Careful!

We can't just square each part.

4x² + 1 is wrong.

The middle part is missing.

Careful: not (2x + 1)² = 4x² + 1 ✗

So we write the bracket two times.

= (2x + 1)(2x + 1)

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 1.

Each one takes the whole second bracket.

= 2x(2x + 1) + 1(2x + 1)

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(1) + 1(2x) + 1(1)

2x times 2x is 4x².

2x times 1 is 2x.

1 times 2x is 2x.

1 times 1 is 1.

= 4x² + 2x + 2x + 1

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

2x + 2x is 4x.

It is like 2 apples plus 2 apples: that is 4 apples.

2x + 2x = 4x

So the expression is 4x² + 4x + 1.

= 4x² + 4x + 1

5 Check

Let's check.

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

We put it into the start.

Start: (2 × 2 + 1)² = (5)² = 25

Now into our answer.

Answer: 4 × 2² + 4 × 2 + 1 = 16 + 8 + 1

= 25

Both give 25.

Same value, so 4x² + 4x + 1 is right!

Both give 25

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