Practice Expression Simplification in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick 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.

Showing a random 20 of 50 problems.

Example 1

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

Example 2

easy
Simplify 5+3xโˆ’25 + 3x - 2.

Example 3

medium
Simplify 5x05x^0 for xโ‰ 0x \neq 0.

Example 4

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

Example 5

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

Example 6

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

Example 7

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

Example 8

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

Example 9

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

Example 10

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

Example 11

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

Example 12

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

Example 13

hard
Simplify x4y6\sqrt{x^4 y^6} for x,y>0x, y > 0.

Example 14

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

Example 15

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

Example 16

easy
Simplify 7aโˆ’2a+a7a - 2a + a.

Example 17

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

Example 18

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

Example 19

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

Example 20

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