Simplify (2x + 1)(x + 3) Step by Step

Step by step

The question

Question: simplify (2x + 1)(x + 3).

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

(2x + 1)(x + 3)

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 2x and 1.

Each one takes the whole second bracket.

= 2x(x + 3) + 1(x + 3)

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.

= 2x(x) + 2x(3) + 1(x) + 1(3)

2x times x is 2x².

2x times 3 is 6x.

1 times x is x.

1 times 3 is 3.

= 2x² + 6x + x + 3

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

6x + x is 7x.

It is like 6 apples plus 1 apple: that is 7 apples.

6x + x = 7x

So the expression is 2x² + 7x + 3.

= 2x² + 7x + 3

4 Check

Let's check.

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

We put it into the start.

Start: (2 × 2 + 1)(2 + 3) = (5)(5) = 25

Now into our answer.

Answer: 2 × 2² + 7 × 2 + 3 = 8 + 14 + 3

= 25

Both give 25.

Same value, so 2x² + 7x + 3 is right!

Both give 25

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer