Factoring Difference of Squares Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Factoring Difference of Squares.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Recognizing and factoring expressions of the form a^2 - b^2 into the product (a + b)(a - b).
When you multiply (a + b)(a - b), the middle terms cancel: a^2 - ab + ab - b^2 = a^2 - b^2. So any time you see a perfect square minus a perfect square, you can instantly factor it. Think of it as a rectangle whose area is the difference of two square areas.
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: The pattern works because the cross terms always cancel. Both terms must be perfect squares separated by subtraction.
Common stuck point: A SUM of squares a^2 + b^2 does NOT factor over the real numbers. This pattern only works for differences.
Sense of Study hint: Ask yourself: is each term a perfect square? Is there a minus sign between them? If both yes, apply the pattern.
Worked Examples
Example 1
easySolution
- 1 Step 1: Recognize the form a^2 - b^2 where a = x and b = 7.
- 2 Step 2: Apply the formula: (a+b)(a-b) = (x+7)(x-7).
- 3 Step 3: Verify: (x+7)(x-7) = x^2 - 7x + 7x - 49 = x^2 - 49 ✓
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardBackground Knowledge
These ideas may be useful before you work through the harder examples.