Practice Rewriting Expressions in Math

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

Quick Recap

Transforming an algebraic expression into a different but mathematically equivalent form to reveal new information.

2(x+3)2(x + 3) and 2x+62x + 6 look different but are the sameβ€”rewriting shows this.

Showing a random 20 of 50 problems.

Example 1

hard
Rewrite x2βˆ’10x+7x^2-10x+7 by completing the square.

Example 2

easy
Rewrite x2β‹…x3x^2\cdot x^3 using one exponent.

Example 3

medium
Rewrite x2+6xx^2+6x by completing the square.

Example 4

medium
Rewrite (x+1)2(x+1)^2 without parentheses.

Example 5

medium
Rewrite 3x+2x\frac{3}{x}+\frac{2}{x} as a single fraction.

Example 6

medium
Rewrite x2βˆ’4xβˆ’2\frac{x^2 - 4}{x - 2} in simplified form.

Example 7

easy
Rewrite x2βˆ’25x^2 - 25 in factored form.

Example 8

hard
Expand (a+b+c)2(a+b+c)^2.

Example 9

easy
Write 5x+2x5x+2x as one term.

Example 10

medium
Factor x2+7x+12x^2+7x+12.

Example 11

medium
Rewrite 50\sqrt{50} in simplest radical form.

Example 12

easy
Are 2x+62x+6 and 2(x+3)2(x+3) equivalent?

Example 13

medium
Rewrite x2βˆ’9xβˆ’3\frac{x^2-9}{x-3} in simpler form (assume xβ‰ 3x\ne 3).

Example 14

medium
Expand (2x+1)(xβˆ’3)(2x+1)(x-3).

Example 15

medium
Simplify x2βˆ’9x+3\tfrac{x^2-9}{x+3} for xβ‰ βˆ’3x\ne -3.

Example 16

hard
Rewrite 2x+3x+1\tfrac{2}{x}+\tfrac{3}{x+1} as a single fraction.

Example 17

easy
Rewrite x+x+xx+x+x as a single term.

Example 18

medium
Simplify 3(x+2)βˆ’2(xβˆ’1)3(x+2)-2(x-1).

Example 19

easy
Rewrite 3(x+4)3(x + 4) in expanded form.

Example 20

easy
Combine like terms: 4x+3βˆ’x+84x+3-x+8.