Factoring Perfect Square Binomials

The video tutorial explores the concept of perfect squares and their role in factoring binomials. It explains how to identify perfect squares in numbers and variables, and demonstrates the pattern for factoring binomials with perfect squares using the difference of squares method. The tutorial provides several examples to illustrate the process, emphasizing the importance of checking for a greatest common factor (GCF) before factoring. It also highlights the limitations of using perfect square factoring when addition is involved, as the method only applies to subtraction.

What is a perfect square?

• A number that is always even

• A number that is the product of a number multiplied by itself

• A number that can be divided by 2

• A number that is always odd

Which of the following is a perfect square?

• 15

• 20

• 25

• 30

What is the result of multiplying (f - l) by (f + l)?

• f^2 + l^2

• f^2 + 2fl + l^2

• f^2 - l^2

• 2fl

When factoring x^2 - 81, what are the factors?

• (x - 7)(x + 7)

• (x - 8)(x + 8)

• (x - 6)(x + 6)

• (x - 9)(x + 9)

What are the factors of 4x^2 - 25?

• (2x - 5)(2x + 5)

• (2x - 4)(2x + 4)

• (4x - 5)(4x + 5)

• (2x - 3)(2x + 3)

How do you factor 16x^2 - 49y^2?

• (3x - 7y)(3x + 7y)

• (3x - 6y)(3x + 6y)

• (4x - 6y)(4x + 6y)

• (4x - 7y)(4x + 7y)

What should you always check for first when factoring binomials?

• Perfect squares

• Addition

• Subtraction

• Greatest common factor (GCF)

What is the GCF of 18x^5 and 32x?

• 2

• 2x

• x

• 4x

Why can't you factor 3x^2 + 12 using the perfect square pattern?

• Because it is addition, not subtraction

• Because x^2 is not a perfect square

• Because 12 is not a perfect square

• Because 3 is not a perfect square

What is the correct factorization of 3(x^2 + 4)?

• (x - 2)(x + 2)

• (x^2 - 4)

• 3(x - 2)(x + 2)

• 3(x^2 + 4)