Expression Simplification Examples in Math

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

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

Concept Recap

Rewriting an algebraic expression into an equivalent but reduced or more organized form by combining like terms and applying identities.

Combine like terms, reduce fractions, apply identities to clean up expressions.

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: Simplifying rewrites an expression into an equivalent, tidier form without changing what it equals.

Common stuck point: The procedure for expression simplification is the easy part; the trap is combining unlike terms like 3x2+5x3x^2+5x into one term. Asking "Am I making one expression cleaner without changing its value (no equation to solve)?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I making one expression cleaner without changing its value (no equation to solve)?

Worked Examples

Example 1

easy
Simplify 6x+3โˆ’2x+56x + 3 - 2x + 5.

Answer

4x+84x + 8

First step

1
Group like terms: (6xโˆ’2x)+(3+5)(6x - 2x) + (3 + 5).

Full solution

  1. 2
    Combine: 4x+84x + 8.
  2. 3
    The expression is now in simplest form.
Simplification combines like terms to produce the most compact equivalent form. Like terms must have the same variable with the same exponent.

Example 2

medium
Simplify 3(2x+4)โˆ’5(xโˆ’1)3(2x + 4) - 5(x - 1).

Example 3

easy
Simplify 2(3xโˆ’1)โˆ’3(xโˆ’2)2(3x-1)-3(x-2).

Example 4

medium
Simplify x5x2\frac{x^5}{x^2}.

Example 5

medium
Simplify 6x2+9x3x\dfrac{6x^2+9x}{3x}.

Example 6

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

Example 7

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

Example 8

hard
Simplify x2โˆ’xโˆ’6x2โˆ’4\dfrac{x^2-x-6}{x^2-4}.

Example 9

hard
Simplify 50+18\sqrt{50}+\sqrt{18}.

Example 10

hard
Simplify 1xโˆ’1โˆ’1x+1\dfrac{1}{x-1} - \dfrac{1}{x+1}.

Example 11

challenge
Simplify the complex fraction 1x+1y1xy\dfrac{\dfrac{1}{x} + \dfrac{1}{y}}{\dfrac{1}{xy}}.

Practice Problems

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

Example 1

easy
Simplify 8yโˆ’3y+y8y - 3y + y.

Example 2

hard
Simplify 2x2+3xโˆ’x2+5xโˆ’42x^2 + 3x - x^2 + 5x - 4.

Example 3

easy
Simplify 3x+5x3x + 5x.

Example 4

easy
Simplify 7aโˆ’2a+a7a - 2a + a.

Example 5

easy
Simplify 4x+3+2x+54x + 3 + 2x + 5.

Example 6

easy
Simplify 2(x+4)2(x + 4).

Example 7

easy
Simplify 6x2\frac{6x}{2}.

Example 8

easy
Simplify x2+2x2x^2 + 2x^2.

Example 9

easy
Simplify 5+3xโˆ’25 + 3x - 2.

Example 10

easy
Simplify x+31\frac{x+3}{1}.

Example 11

medium
Simplify 3(x+2)+4x3(x + 2) + 4x.

Example 12

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

Example 13

medium
Simplify 4x+84\frac{4x + 8}{4}.

Example 14

medium
Simplify 5x2+3xโˆ’2x2+x5x^2 + 3x - 2x^2 + x.

Example 15

medium
Simplify (x+3)(x+2)(x + 3)(x + 2).

Example 16

medium
Simplify x2+3xx\frac{x^2 + 3x}{x} for xโ‰ 0x \ne 0.

Example 17

medium
Simplify โˆ’2(xโˆ’5)+3(2x+1)-2(x - 5) + 3(2x + 1).

Example 18

medium
Simplify 3x+2yโˆ’x+4y3x + 2y - x + 4y.

Example 19

medium
Simplify (2x)2+3x2(2x)^2 + 3x^2.

Example 20

challenge
For which constant kk does 3(x+k)+2x3(x + k) + 2x simplify to 5x+125x + 12?

Example 21

challenge
Simplify x2โˆ’9x+3\frac{x^2 - 9}{x + 3} for xโ‰ โˆ’3x \ne -3.

Example 22

challenge
Show that (x+3)2โˆ’(xโˆ’3)2(x + 3)^2 - (x - 3)^2 simplifies to 12x12x.

Example 23

easy
Simplify 9x+4โˆ’3xโˆ’19x + 4 - 3x - 1.

Example 24

easy
Simplify 4(x+3)+2x4(x+3) + 2x.

Example 25

easy
Simplify 3a+5bโˆ’a+2b3a + 5b - a + 2b.

Example 26

easy
Simplify 7x2โˆ’3x2+x27x^2 - 3x^2 + x^2.

Example 27

easy
Simplify xโ‹…xโ‹…xx \cdot x \cdot x.

Example 28

medium
Simplify (2x3)(5x4)(2x^3)(5x^4).

Example 29

medium
Simplify (3x2)3(3x^2)^3.

Example 30

medium
Simplify x3+x6\frac{x}{3} + \frac{x}{6}.

Example 31

medium
Simplify 15x4y25x2y\dfrac{15x^4 y^2}{5x^2 y}.

Example 32

medium
Simplify x2โˆ’9xโˆ’3\dfrac{x^2-9}{x-3} for xโ‰ 3x \neq 3.

Example 33

hard
Simplify 2x+3x+1\dfrac{2}{x} + \dfrac{3}{x+1}.

Example 34

hard
Simplify (2xโˆ’3)2(2x-3)^2.

Example 35

hard
Simplify x4y6\sqrt{x^4 y^6} for x,y>0x, y > 0.
โ† Back to Expression Simplification Formula Explained Practice Mode

Background Knowledge

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

expressionssimplifying rational expressions