Rewriting Expressions Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Rewriting 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
Transforming an algebraic expression into a different but mathematically equivalent form to reveal new information.
2(x + 3) and 2x + 6 look different but are the same—rewriting shows this.
Read the full concept explanation →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: Different forms reveal different information: factored shows zeros, expanded shows terms.
Common stuck point: Choosing which form to rewrite into — factored, expanded, or simplified — depends on what the problem is asking.
Sense of Study hint: Ask yourself: what information do I need? Then pick the form (factored, expanded, simplified) that reveals it.
Worked Examples
Example 1
easySolution
- 1 Recognize as a difference of squares: x^2 - 5^2.
- 2 Apply the pattern: a^2 - b^2 = (a+b)(a-b).
- 3 Result: (x+5)(x-5).
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.