Expressions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Expressions.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A combination of numbers, variables, and operations (like addition, subtraction, multiplication, division) that represents a mathematical quantity. Unlike equations, expressions do not contain an equals sign and cannot be solved โ€” they can only be simplified or evaluated.

A recipe for calculating a value: '2x+32x + 3' tells you to double xx and add 3.

Read the full concept explanation โ†’

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: An expression is a combination of numbers, variables, and operations that names a value but makes no claim.

Common stuck point: The procedure for expressions is the easy part; the trap is trying to solve an expression. Asking "Is there a combination of terms with NO equals sign, so the only moves are simplify or evaluate?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is there a combination of terms with NO equals sign, so the only moves are simplify or evaluate?

Worked Examples

Example 1

easy
Simplify the expression 4x+3xโˆ’24x + 3x - 2.

Answer

7xโˆ’27x - 2

First step

1
Identify like terms: 4x4x and 3x3x both contain xx.

Full solution

  1. 2
    Combine like terms: 4x+3x=7x4x + 3x = 7x.
  2. 3
    The simplified expression is 7xโˆ’27x - 2.
Like terms have the same variable raised to the same power. They can be combined by adding their coefficients while keeping the variable part unchanged.

Example 2

medium
Evaluate 2a2โˆ’3a+12a^2 - 3a + 1 when a=3a = 3.

Example 3

medium
Simplify 2(x+4)+3(xโˆ’1)2(x + 4) + 3(x - 1).

Example 4

medium
Write an expression for: 'half of a number, plus seven'.

Example 5

hard
Expand (x+3)(x+5)(x + 3)(x + 5).

Example 6

hard
Expand and simplify (2xโˆ’3)2(2x - 3)^2.

Example 7

challenge
Simplify (x+2)(xโˆ’2)โˆ’(xโˆ’1)2(x + 2)(x - 2) - (x - 1)^2.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Simplify 5y+2โˆ’3y+75y + 2 - 3y + 7.

Example 2

medium
Write an algebraic expression for: 'triple a number, then subtract 4.'

Example 3

easy
Is 4x+74x + 7 an expression or an equation?

Example 4

easy
Simplify 3x+2x3x + 2x.

Example 5

easy
Evaluate 2a+32a + 3 when a=5a = 5.

Example 6

easy
How many terms are in 5xโˆ’2y+75x - 2y + 7?

Example 7

easy
Simplify x+3+2x+1x + 3 + 2x + 1.

Example 8

easy
Write 'twice a number, minus 55' as an expression.

Example 9

easy
Apply the distributive property: 3(x+4)3(x + 4).

Example 10

easy
Are 2x2x and 2y2y like terms?

Example 11

medium
Simplify 2(3xโˆ’1)+4x2(3x - 1) + 4x.

Example 12

medium
Simplify 5โˆ’2(xโˆ’3)5 - 2(x - 3).

Example 13

medium
Evaluate a2โˆ’b2\frac{a^2 - b}{2} at a=4,b=6a = 4, b = 6.

Example 14

medium
Simplify 3x+2(xโˆ’y)โˆ’y3x + 2(x - y) - y.

Example 15

medium
Factor out the common factor: 6x+86x + 8.

Example 16

medium
Write an expression for the perimeter of a rectangle with length LL and width Lโˆ’2L - 2.

Example 17

medium
Why can 3x+23x + 2 not be simplified to 5x5x?

Example 18

challenge
Simplify x2โˆ’4x+2\frac{x^2 - 4}{x + 2} for xโ‰ โˆ’2x \ne -2.

Example 19

challenge
Expand and simplify (x+3)(xโˆ’3)(x + 3)(x - 3).

Example 20

challenge
Simplify 2x+3x2\frac{2}{x} + \frac{3}{x^2} into a single fraction.

Example 21

medium
Simplify 6x+93\frac{6x + 9}{3}.

Example 22

medium
Combine: 4abโˆ’ab+2ab4ab - ab + 2ab.

Example 23

easy
Simplify 6xโˆ’2x+36x - 2x + 3.

Example 24

easy
Evaluate 5nโˆ’25n - 2 when n=6n = 6.

Example 25

easy
Apply the distributive property: 5(2xโˆ’3)5(2x - 3).

Example 26

medium
Evaluate x2+2xโˆ’5x^2 + 2x - 5 when x=โˆ’2x = -2.

Example 27

medium
Simplify 4(2xโˆ’1)โˆ’3(x+2)4(2x - 1) - 3(x + 2).

Example 28

medium
Combine like terms: 3a+4bโˆ’a+2b3a + 4b - a + 2b.

Example 29

medium
Evaluate 3(x+y)23(x + y)^2 when x=1,y=2x = 1, y = 2.

Example 30

hard
Simplify 6x2+4x2x\frac{6x^2 + 4x}{2x} assuming xโ‰ 0x \ne 0.

Example 31

hard
Simplify 2(3xโˆ’4)โˆ’(xโˆ’5)2(3x - 4) - (x - 5).

Example 32

medium
Evaluate 2xโˆ’1x+3\frac{2x - 1}{x + 3} when x=4x = 4.

Example 33

medium
Write an expression: 'the product of 44 and the sum of xx and 77'.

Example 34

easy
Simplify โˆ’3x+5x-3x + 5x.

Example 35

medium
Evaluate a+bโˆ’aba + b - ab when a=5,b=2a = 5, b = 2.

Example 36

medium
Simplify 12(4x+6)โˆ’x\frac{1}{2}(4x + 6) - x.

Example 37

hard
A rectangle has length x+4x + 4 and width xx. Write an expression for the area.

Example 38

easy
Simplify 7+2xโˆ’3+x7 + 2x - 3 + x.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

variablesorder of operations