Simplify (x - 5)(x - 1) Step by Step

Step by step

The question

Question: simplify (x − 5)(x − 1).

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

(x − 5)(x − 1)

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 − 1) − 5(x − 1)

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(−1) + (−5)(x) + (−5)(−1)

− × − = +

Watch the signs.

x times x is x².

x times (−1) is −x.

(−5) times x is −5x.

(−5) times (−1) is 5.

= x² − x − 5x + 5

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

−x − 5x is −6x.

−x − 5x = −6x

So the expression is x² − 6x + 5.

= x² − 6x + 5

4 Check

Let's check.

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

We put it into the start.

Start: (2 − 5)(2 − 1) = (−3)(1) = −3

Now into our answer.

Answer: 2² − 6 × 2 + 5 = 4 − 12 + 5 = −3

Both give −3.

Same value, so x² − 6x + 5 is right!

Both give −3

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer