Expansion Intuition Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Expansion Intuition.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Understanding algebraic expansion as the process of applying the distributive property to multiply out factors and remove parentheses.
Open up the parentheses: (x + 2)(x + 3) becomes x^2 + 3x + 2x + 6 = x^2 + 5x + 6.
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: Expansion applies the distributive property to remove parentheses.
Common stuck point: FOIL is just a memory aid for distributing two binomials — it is not a new rule, just one application of distribution.
Sense of Study hint: Draw arrows from each term in the first factor to each term in the second to make sure nothing is missed.
Worked Examples
Example 1
easySolution
- 1 Use FOIL: First: x \cdot x = x^2. Outer: x \cdot 5 = 5x. Inner: 3 \cdot x = 3x. Last: 3 \cdot 5 = 15.
- 2 Combine: x^2 + 5x + 3x + 15 = x^2 + 8x + 15.
- 3 Notice: 3 + 5 = 8 (middle coefficient) and 3 \times 5 = 15 (constant).
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.