Factoring and Perfect Square Trinomials

This video tutorial focuses on factoring complex algebraic expressions, particularly perfect square trinomials and the difference of squares method. It begins with an introduction to the concept of factoring and perfect square trinomials, followed by detailed steps to identify and factor these expressions. The tutorial includes multiple example problems, demonstrating the application of these methods to factor complex and multi-variable expressions. The video aims to enhance understanding of algebraic factoring techniques through practical examples and step-by-step explanations.

What is the formula for a perfect square trinomial?

• a^2 + 2ab + b^2

• a^2 + ab + b^2

• a^2 - ab + b^2

• a^2 - 2ab + b^2

How can you verify if an expression is a perfect square trinomial?

• By checking if the middle term is the sum of the square roots of the first and last terms

• By checking if the middle term is twice the product of the square roots of the first and last terms

• By checking if the middle term is half the product of the square roots of the first and last terms

• By checking if the middle term is the difference of the square roots of the first and last terms

What is the result of factoring x^2 - 25 using the difference of squares method?

• (x - 5)(x + 5)

• (x - 5)(x - 5)

• (x + 5)(x + 5)

• (x + 5)(x - 5)

Which method is used to factor expressions like a^2 - b^2?

• Completing the square

• Quadratic formula

• Difference of squares method

• Perfect square trinomial method

What is the first step in factoring the expression 4a^2 - 20ab + 25b^2 - 100?

• Identify it as a perfect square trinomial

• Use the quadratic formula

• Apply the difference of squares method

• Factor by grouping

How do you factor the expression 4a^2 - 20ab + 25b^2?

• (4a - 5b)^2

• (2a + 5b)^2

• (2a - 5b)^2

• (4a + 5b)^2

What is the final step in factoring the expression 4x^2 + 12xy + 9y^2 - 9r^2 - 24rs + 16s^2?

• Apply the quadratic formula

• Use the difference of squares method

• Factor by grouping

• Complete the square

What is the result of factoring 9r^2 + 24rs + 16s^2?

• (3r + 4s)^2

• (3r - 4s)^2

• (9r - 4s)^2

• (9r + 4s)^2

Which expression represents the difference of squares for 2x + 3y and 3r + 4s?

• (2x + 3y + 3r + 4s)(2x + 3y - 3r - 4s)

• (2x - 3y + 3r - 4s)(2x - 3y - 3r + 4s)

• (2x - 3y + 3r + 4s)(2x - 3y - 3r - 4s)

• (2x + 3y + 3r - 4s)(2x + 3y - 3r + 4s)

What is the square root of 16s^2?

• 5s

• 4s

• 3s

• 2s