Learn how to use formulas after taking out common factors and how to simplify calculations by using factoring.
Complex factoring
First take out the common factor, then apply another 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 calculation)
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 taking out common factors
- Factoring can simplify complicated numerical calculations
- 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