Simplify (x + 5)(x - 5) Step by Step

Step by step

The question

Question: simplify (x + 5)(x − 5).

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

(x + 5)(x − 5)

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 5.

Each one takes the whole second bracket.

= x(x − 5) + 5(x − 5)

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(−5) + 5(x) + 5(−5)

− × + = −

Watch the signs.

x times x is x².

x times (−5) is −5x.

5 times x is 5x.

5 times (−5) is −25.

= x² − 5x + 5x − 25

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

−5x + 5x is 0.

−5x + 5x = 0

So the expression is x² − 25.

= x² − 25

4 Check

Let's check.

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

We put it into the start.

Start: (2 + 5)(2 − 5) = (7)(−3) = −21

Now into our answer.

Answer: 2² − 25 = 4 − 25 = −21

Both give −21.

Same value, so x² − 25 is right!

Both give −21

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer