Expand and simplify (x + 4)(x + 3). Step by Step

Step by step

The question

Question: simplify (x + 4)(x + 3).

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

(x + 4)(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 x and 4.

Each one takes the whole second bracket.

= x(x + 3) + 4(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.

= x(x) + x(3) + 4(x) + 4(3)

x times x is x²: x squared.

x × x = x²

x times 3 is 3x.

4 times x is 4x.

4 times 3 is 12.

= x² + 3x + 4x + 12

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

3x + 4x is 7x.

3x + 4x = 7x

So the expression is x² + 7x + 12.

= x² + 7x + 12

4 Check

Let's check.

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

Any number works, and a small one keeps the sums easy.

We put it into the question.

Question: (2 + 4)(2 + 3) = (6)(5) = 30

Now into our answer.

Answer: 2² + 7 × 2 + 12 = 4 + 14 + 12 = 30

Both give 30.

Same value, so x² + 7x + 12 is right!

Both give 30

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer