📚 Topic Summary
Factorising algebraic expressions is like reverse engineering multiplication. Instead of multiplying terms together to expand an expression, you're breaking it down into its constituent factors. This often involves identifying common factors within the expression and rewriting it as a product of those factors. It's a fundamental skill in algebra, used for simplifying expressions, solving equations, and understanding mathematical relationships.
🧠 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Factor |
A. An expression with one term. |
| 2. Expression |
B. A value that, when multiplied by itself, equals a given number. |
| 3. Monomial |
C. A number or algebraic quantity that divides another number or expression evenly. |
| 4. Square Root |
D. A mathematical phrase containing numbers, variables, and operators. |
| 5. Constant |
E. A fixed value that does not change. |
✍️ Part B: Fill in the Blanks
Factorising is the _________ of expanding. To factorise, we look for the _________ common factor. For example, in the expression $2x + 4$, the highest common factor is _________. Therefore, we can factorise it as $_________$. Factorising simplifies solving _________ .
🤔 Part C: Critical Thinking
Explain, in your own words, why factorising is a useful skill in algebra.