Factoring Techniques and Applications

This video tutorial explains how to factor the difference of two squares using a specific formula. It covers basic and advanced examples, including expressions with higher degree polynomials and special cases. The tutorial also demonstrates factoring using the greatest common factor (GCF) and addresses complex expressions with multiple terms. Additionally, it provides guidance on handling fractional expressions. By the end of the video, viewers will understand how to factor a variety of expressions involving the difference of two squares.

What is the factored form of x² - 36?

• (x + 18)(x - 18)

• (x + 9)(x - 9)

• (x + 6)(x - 6)

• (x + 3)(x - 3)

How would you factor 4x² - 25?

• (4x + 5)(4x - 5)

• (2x + 5)(2x - 5)

• (x + 5)(x - 5)

• (2x + 25)(2x - 25)

What is the first step in factoring 3x² - 27 using the difference of squares?

• Find the square root of 3

• Factor out the GCF

• Apply the difference of squares formula directly

• Multiply by 3

Which of the following is the factored form of x⁴ - 81?

• (x² + 81)(x² - 81)

• (x + 9)(x - 9)

• (x² + 9)(x² - 9)

• (x² + 3)(x² - 3)

How do you factor 16x⁴ - 81y⁴?

• (4x² + 9y²)(4x² - 9y²)

• (16x² + 81y²)(16x² - 81y²)

• (4x + 9y)(4x - 9y)

• (x² + 9y²)(x² - 9y²)

What is the factored form of 144x⁶ - 225y⁴?

• (12x³ + 15y²)(12x³ - 15y²)

• (144x³ + 225y²)(144x³ - 225y²)

• (12x² + 15y²)(12x² - 15y²)

• (x³ + y²)(x³ - y²)

How would you factor 4x²y⁶ - 25?

• (2x²y³ + 5)(2x²y³ - 5)

• (xy³ + 5)(xy³ - 5)

• (2xy³ + 5)(2xy³ - 5)

• (4xy³ + 25)(4xy³ - 25)

What is the factored form of 36 - (x + y)²?

• (6 + x + y)(6 - x - y)

• (x + y + 6)(x + y - 6)

• (36 + x + y)(36 - x - y)

• (6 + x - y)(6 - x + y)

How do you factor (x + 3)² - 16?

• (x + 3 + 4)(x + 3 - 4)

• (x + 3 + 16)(x + 3 - 16)

• (x + 4)(x - 4)

• (x + 3 + 2)(x + 3 - 2)

What is the factored form of a difference of squares in fraction form, such as (4a⁶/9) - (49b²c⁸/121)?

• (2a³/3 + 49b²c⁴/11)(2a³/3 - 49b²c⁴/11)

• (4a³/9 + 49b²c⁴/121)(4a³/9 - 49b²c⁴/121)

• (2a³/3 + 7bc⁴/11)(2a³/3 - 7bc⁴/11)

• (a³/3 + 7bc⁴/11)(a³/3 - 7bc⁴/11)