📚 Topic Summary
The difference of squares is a special pattern you'll find in algebra. It appears when you have two perfect squares separated by a subtraction sign. The expression looks like this: $a^2 - b^2$. Factoring it is super straightforward: it always breaks down into $(a + b)(a - b)$. This works because when you expand $(a + b)(a - b)$, the middle terms cancel out, leaving you with just $a^2 - b^2$. Knowing this pattern saves you a ton of time when factoring!
🧠 Part A: Vocabulary
Match each term with its definition:
| Term |
Definition |
| 1. Perfect Square |
A. The process of breaking down an expression into its factors. |
| 2. Factor |
B. A number or expression that is multiplied by another to get a product. |
| 3. Difference of Squares |
C. A number that can be obtained by squaring an integer. |
| 4. Factoring |
D. $a^2 - b^2$, which factors to $(a + b)(a - b)$. |
| 5. Expression |
E. A combination of variables, numbers, and operators. |
✍️ Part B: Fill in the Blanks
The difference of squares pattern is a useful shortcut in __________. It applies when you have two ________ __________ separated by a __________ sign. The general form is $a^2 - b^2$, which factors into (a + b)(a - b). This works because when you ________ (a + b)(a - b), the middle terms __________ out.
🤔 Part C: Critical Thinking
Explain in your own words why the difference of squares pattern only works when there is a subtraction sign between the two terms and not an addition sign. What happens if you try to factor $a^2 + b^2$ using the same method?