Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Expressions, exponents and radicals

Example 12 from Algebra and Trigonometry, 1.1 Real Numbers: Algebra Essentials

Simplifying Algebraic Expressions

Simplify each algebraic expression.

ⓐ $3 x - 2 y + x - 3 y - 7$
ⓑ $2 r - 5 (3 - r) + 4$
ⓒ $(4 t - \frac{5}{4} s) - (\frac{2}{3} t + 2 s)$
ⓓ $2 m n - 5 m + 3 m n + n$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ
  $\begin{matrix} 3 x - 2 y + x - 3 y - 7 & = & 3 x + x - 2 y - 3 y - 7 & Commutative property of addition. \\ = & 4 x - 5 y - 7 & Simplify. \end{matrix}$
2. ⓑ
  $\begin{matrix} 2 r - 5 (3 - r) + 4 & = & 2 r - 15 + 5 r + 4 & Distributive property. \\ = & 2 r + 5 r - 15 + 4 & Commutative property of addition. \\ = & 7 r - 11 & Simplify. \end{matrix}$
3. ⓒ
  $\begin{matrix} (4 t - \frac{5}{4} s) - (\frac{2}{3} t + 2 s) & = & 4 t - \frac{5}{4} s - \frac{2}{3} t - 2 s & Distributive property. \\ = & 4 t - \frac{2}{3} t - \frac{5}{4} s - 2 s & Commutative property of addition. \\ = & \frac{10}{3} t - \frac{13}{4} s & Simplify. \end{matrix}$
4. ⓓ
  $\begin{matrix} 2 m n - 5 m + 3 m n + n & = & 2 m n + 3 m n - 5 m + n & Commutative property of addition. \\ = & 5mn-5m+n & Simplify. \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify each algebraic expression.

ⓐ $\frac{2}{3} y - 2 (\frac{4}{3} y + z)$
ⓑ $\frac{5}{t} - 2 - \frac{3}{t} + 1$
ⓒ $4 p (q - 1) + q (1 - p)$
ⓓ $9 r - (s + 2 r) + (6 - s)$

How did it go?

PreviousUsing a Formula Next Simplifying a Formula

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.