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

Step by step

The question

Question: simplify (x + 2)(x² − x + 1).

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

(x + 2)(x² − 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 2.

Each one takes the whole second bracket.

= x(x² − x + 1) + 2(x² − 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(x²) + x(−x) + x(1) + 2(x²) + 2(−x) + 2(1)

− × + = −

Watch the signs.

x times x² is x³.

x times (−x) is −x².

x times 1 is x.

2 times x² is 2x².

= x³ − x² + x + 2x² − 2x + 2

3 Group like terms

Terms are the parts between the + and − signs.

Like terms are the same kind: same letters, same powers.

All the x² terms go together.

Each colour is one kind.

like terms = same letters,

same powers

We move like terms next to each other.

Each term takes its sign with it.

= x³ − x² + 2x² + x − 2x + 2

−x² + 2x² is x².

x − 2x is −x.

It is like 1 apple take away 2 apples: that is 1 apple.

−x² + 2x² = x²

x − 2x = −x

So the expression is x³ + x² − x + 2.

= x³ + x² − x + 2

4 Check

Let's check.

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

We put it into the start.

Start: (2 + 2)(2² − 2 + 1) = (4)(3) = 12

Now into our answer.

Answer: 2³ + 2² − 2 + 2 = 8 + 4 − 2 + 2

= 12

Both give 12.

Same value, so x³ + x² − x + 2 is right!

Both give 12

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer