Learn how to factor out common factors before applying formulas, and how to simplify calculations using factoring.
Complex Factoring
First factor out the common factor, then apply a formula to the remaining expression.
📘 Example ①
Factor 2x² − 8.
Answer:2x² − 8 = 2(x² − 4) = 2(x + 2)(x − 2)
Factor 2x² − 8.
Answer:2x² − 8 = 2(x² − 4) = 2(x + 2)(x − 2)
📘 Example ② (Application to Calculations)
Calculate 102² − 98² using factoring.
Answer:102² − 98² = (102 + 98)(102 − 98) = 200 × 4 = 800
Calculate 102² − 98² using factoring.
Answer:102² − 98² = (102 + 98)(102 − 98) = 200 × 4 = 800
💡 Key Points
- Always begin factoring by factoring out common factors
- Factoring makes complex numerical calculations easier
- Factoring is also useful when finding the value of an algebraic expression
Practice Problems
- Factor 3x² − 12.
- Calculate 51² − 49² using factoring.
Answers and Explanations
- Answer:3x² − 12 = 3(x² − 4) = 3(x + 2)(x − 2)
- Answer:51² − 49² = (51 + 49)(51 − 49) = 100 × 2 = 200