Simplify (x + 1)(x - 4) Step by Step

Step by step

The question

Question: simplify (x + 1)(x − 4).

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

(x + 1)(x − 4)

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 1.

Each one takes the whole second bracket.

= x(x − 4) + 1(x − 4)

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(−4) + 1(x) + 1(−4)

− × + = −

Watch the signs.

x times x is x².

x times (−4) is −4x.

1 times x is x.

1 times (−4) is −4.

= x² − 4x + x − 4

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

−4x + x is −3x.

−4x + x = −3x

So the expression is x² − 3x − 4.

= x² − 3x − 4

4 Check

Let's check.

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

We put it into the start.

Start: (2 + 1)(2 − 4) = (3)(−2) = −6

Now into our answer.

Answer: 2² − 3 × 2 − 4 = 4 − 6 − 4 = −6

Both give −6.

Same value, so x² − 3x − 4 is right!

Both give −6

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer