Simplify (3x - 2)(2x + 5) Step by Step

Step by step

The question

Question: simplify (3x − 2)(2x + 5).

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

(3x − 2)(2x + 5)

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 3x and −2.

Each one takes the whole second bracket.

= 3x(2x + 5) − 2(2x + 5)

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.

= 3x(2x) + 3x(5) + (−2)(2x) + (−2)(5)

− × + = −

Watch the signs.

3x times 2x is 6x².

3x times 5 is 15x.

(−2) times 2x is −4x.

(−2) times 5 is −10.

= 6x² + 15x − 4x − 10

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

15x − 4x is 11x.

It is like 15 apples take away 4 apples: that is 11 apples.

15x − 4x = 11x

So the expression is 6x² + 11x − 10.

= 6x² + 11x − 10

4 Check

Let's check.

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

We put it into the start.

Start: (3 × 2 − 2)(2 × 2 + 5) = (4)(9) = 36

Now into our answer.

Answer: 6 × 2² + 11 × 2 − 10

= 24 + 22 − 10 = 36

Both give 36.

Same value, so 6x² + 11x − 10 is right!

Both give 36

Let's look back.

First: split the first bracket.

Then: open the brackets.

Then: group like terms.

Last: check.

Answer