Steply

Simplify expressions

Like terms, open brackets · Algebra 1 · 22 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Open the brackets
  2. Group like terms
  3. Check

The steps for Simplify 3x + 2(x - 4) - 5. Every solution names its steps, so you always know what comes next.

Worked examples

Simplify 3x + 5x Easy

The question

Question: simplify 3x + 5x.

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

3x + 5x

1 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 + 5x is 8x.

It is like 3 apples plus 5 apples: that is 8 apples.

3x + 5x = 8x

So the expression is 8x.

= 8x

2 Check

Let's check.

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

We put it into the start.

Start: 3 × 2 + 5 × 2 = 6 + 10 = 16

Now into our answer.

Answer: 8 × 2 = 16

Both give 16.

Same value, so 8x is right!

Both give 16

Let's look back.

First: group like terms.

Last: check.

Answer
= 8x

▶ Watch it solved

Simplify 3x + 2(x - 4) - 5 Medium

The question

Question: simplify 3x + 2(x − 4) − 5.

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

3x + 2(x − 4) − 5

1 Open the brackets

The 2 in front of the bracket multiplies every part inside.

a(b + c) = ab + ac

So we write 2 times each part.

= 3x + 2(x) + 2(−4) − 5
− × + = −

Watch the signs.

2 times x is 2x.

2 times (−4) is −8.

= 3x + 2x − 8 − 5

2 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.

Plain numbers go together.

Each colour is one kind.

like terms = same letters,
same powers

3x + 2x is 5x.

It is like 3 apples plus 2 apples: that is 5 apples.

−8 − 5 is −13.

3x + 2x = 5x
−8 − 5 = −13

So the expression is 5x − 13.

= 5x − 13

3 Check

Let's check.

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

We put it into the start.

Start: 3 × 2 + 2 × (2 − 4) − 5
= 6 + 2 × (−2) − 5 = 6 + (−4) − 5
= 6 − 4 − 5 = −3

Now into our answer.

Answer: 5 × 2 − 13 = 10 − 13 = −3

Both give −3.

Same value, so 5x − 13 is right!

Both give −3

Let's look back.

First: open the brackets.

Then: group like terms.

Last: check.

Answer
= 5x − 13

▶ Watch it solved

Simplify 5x - (3 - 2x) + 4(x - 1) Harder

The question

Question: simplify 5x − (3 − 2x) + 4(x − 1).

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

5x − (3 − 2x) + 4(x − 1)

1 Open the brackets

The 4 in front of the bracket multiplies every part inside.

A minus in front of a bracket changes the sign of every part inside.

a(b + c) = ab + ac
−( + ) → −, −( − ) → +

So we write 4 times each part.

= 5x − 3 + 2x + 4(x) + 4(−1)
− × + = −

Watch the signs.

4 times x is 4x.

4 times (−1) is −4.

= 5x − 3 + 2x + 4x − 4

2 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.

Plain numbers 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.

= 5x + 2x + 4x − 3 − 4

5x + 2x + 4x is 11x.

−3 − 4 is −7.

5x + 2x + 4x = 11x
−3 − 4 = −7

So the expression is 11x − 7.

= 11x − 7

3 Check

Let's check.

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

We put it into the start.

Start: 5 × 2 − (3 − 2 × 2) + 4 × (2 − 1)
= 10 − (−1) + 4 × 1 = 10 − (−1) + 4
= 10 + 1 + 4 = 15

Now into our answer.

Answer: 11 × 2 − 7 = 22 − 7 = 15

Both give 15.

Same value, so 11x − 7 is right!

Both give 15

Let's look back.

First: open the brackets.

Then: group like terms.

Last: check.

Answer
= 11x − 7

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 3x + 5x
    Answer
    = 8x
  2. 7y - 2y
    Answer
    = 5y
  3. 4a + 3 + 2a
    Answer
    = 6a + 3
  4. 6x + 2 - 4x + 5
    Answer
    = 2x + 7
  5. 5m - m
    Answer
    = 4m
  6. 2(x + 4)
    Answer
    = 2x + 8
  7. 3(2y - 1)
    Answer
    = 6y − 3
  8. 4a + 3b - a + 2b
    Answer
    = 3a + 5b
  9. -(x - 6)
    Answer
    = −x + 6
  10. 2x + x + 4x
    Answer
    = 7x

Medium

  1. 3x + 2(x - 4) - 5
    Answer
    = 5x − 13
  2. 5 - (2x - 3)
    Answer
    = −2x + 8
  3. 2x^2 + 3x - x^2 + 4
    Answer
    = x2 + 3x + 4
  4. 3(2x + 1) - 2(x - 5)
    Answer
    = 4x + 13
  5. 4(a + 2) + 3(a - 1)
    Answer
    = 7a + 5
  6. 6y - 3(y + 2)
    Answer
    = 3y − 6
  7. x/2 + x/3
    Answer
    = 5x6
  8. -2(3x - 4) + 7
    Answer
    = −6x + 15

Harder

  1. 5x - (3 - 2x) + 4(x - 1)
    Answer
    = 11x − 7
  2. 2(x^2 + 3x) - x(x - 1)
    Answer
    = x2 + 7x
  3. 3a + 2b - 4(a - b)
    Answer
    = −a + 6b
  4. x/4 + 3x/2
    Answer
    = 7x4