Chapter Contents

• Factoring and Fractions
• 1. Special Products
• 2. Common Factor and Difference of Squares
• 3. Factoring Trinomials
• 4. The Sum and Difference of Cubes
• 5. Equivalent Fractions
• 6. Multiplication and Division of Fractions
• 7. Addition and Subtraction of Fractions
• 8. Equations Involving Fractions
• Factoring and Fractions Problem Solver

• Comments, Questions?

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2. Common Factor and Difference of Squares

Factoring means writing an expression as the product of its simplest factors.

Example 1: Factoring a number

14 = 7 × 2

[7 and 2 are the simplest factors of 14].

Example 2: Factoring an algebraic expression

3x + 15 = 3(x + 5)

This means that the factors of 3x + 15 are

3 and

(x + 5)

To be able to factor successfully, we need to recognise the formulas from Section 1. So it's a good idea to learn those formulas well!

Factoring Difference of Two Squares

To factor the difference of 2 squares, we just apply the formula given in Section 1 - Special Products in reverse. That is:

x² − y² = (x + y)(x − y)

Example 3: Factoring difference of 2 squares

Factor 36s² − 121t²

Answer

Exercises

Factor the following:

(1) 18p³ − 3p²

Answer

(2) 5a + 10ax − 5ay + 20az

Answer

(3) 36a²b ² − 169c²

Answer

(4) (a − b)² − 1

Answer

(5) y⁴ − 81

Answer

(6) r² − s² + 2st − t²

Answer