Factoring Quadratic Equations with Difference of Squares

The video tutorial explains how to solve quadratic equations by factoring, focusing on the difference of squares method. It provides three examples: X^2 - 9 = 0, 9X^2 - 64 = 0, and 25 - 4X^2 = 0. Each example demonstrates recognizing perfect squares, applying the difference of squares formula, and solving for X. The solutions are presented in both individual and combined forms, such as X = ±3. The tutorial aims to help students understand the factoring process and apply it to similar problems.

How can the solutions x = 3 and x = -3 be represented in a shorter form?

• x = -3

• x = 3

• x = ±3

• x = 0

What is the first step in solving the quadratic equation x^2 - 9 = 0?

• Divide both sides by x

• Multiply both sides by 2

• Add 9 to both sides

• Recognize that x^2 is a perfect square

What are the solutions to the equation x^2 - 9 = 0?

• x = 9 or x = -9

• x = 0

• x = 1 or x = -1

• x = 3 or x = -3

What is the first term in the second example 9x^2 - 64 = 0?

• 81x^2

• 9x^2

• 8x^2

• 64

What is the second term in the second example 9x^2 - 64 = 0?

• 64

• 81

• 9

• 8

What are the solutions to the equation 9x^2 - 64 = 0?

• x = ±8/9

• x = ±9/8

• x = ±2

• x = ±1

What is the first term in the third example 25 - 4x^2 = 0?

• 4x^2

• 2x^2

• 25

• 5x^2

What is the second term in the third example 25 - 4x^2 = 0?

• 25

• 5x^2

• 2x^2

• 4x^2

What are the solutions to the equation 25 - 4x^2 = 0?

• x = ±5

• x = ±1/2

• x = ±2/5

• x = ±5/2

What is the common factorization method used in all three examples?

• Sum of squares

• Difference of squares

• Product of squares

• Quotient of squares