Simplify (x + 4)^2 Step by Step

Step by step

The question

Question: simplify (x + 4)².

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

(x + 4)²

1 Write the square out

A square means the bracket times itself.

(x + 4)² is x + 4 times x + 4.

( )² = ( )( )

Careful!

We can't just square each part.

x² + 16 is wrong.

The middle part is missing.

Careful: not (x + 4)² = x² + 16 ✗

So we write the bracket two times.

= (x + 4)(x + 4)

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 4.

Each one takes the whole second bracket.

= x(x + 4) + 4(x + 4)

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(4) + 4(x) + 4(4)

x times x is x².

x times 4 is 4x.

4 times x is 4x.

4 times 4 is 16.

= x² + 4x + 4x + 16

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

4x + 4x is 8x.

It is like 4 apples plus 4 apples: that is 8 apples.

4x + 4x = 8x

So the expression is x² + 8x + 16.

= x² + 8x + 16

5 Check

Let's check.

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

We put it into the start.

Start: (2 + 4)² = (6)² = 36

Now into our answer.

Answer: 2² + 8 × 2 + 16 = 4 + 16 + 16 = 36

Both give 36.

Same value, so x² + 8x + 16 is right!

Both give 36

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