Factoring a Binomial: Difference of Squares

This video tutorial covers the process of factoring a binomial when there is a difference of squares. It begins with an introduction to the concept, explaining the basic formula A squared minus B squared and how it factors into (A + B)(A - B). The tutorial then provides an example problem, 49 - X squared, and demonstrates two methods for factoring it. The first method keeps the constant term first, while the second method rearranges the terms to have the variable first. Both methods are verified to be correct, and the video concludes with a summary of the key points.

What is the basic formula for factoring a difference of squares?

• (A + B)(A - B)

• (A - B)(A - B)

• (A + B)(A + B)

• (A^2 + B^2)

In the expression 49 - X^2, what are the perfect squares?

• 7 and X^2

• 49 and X^2

• 49 and X

• 7 and X

What is the first step in factoring 49 - X^2 using the difference of squares?

• Multiply the terms

• Identify the perfect squares

• Add the terms

• Subtract the terms

How can 49 - X^2 be rewritten to have the variable term first?

• X^2 - 49

• -X^2 + 49

• 49 + X^2

• -49 + X^2

What happens when you factor out a negative from -X^2 + 49?

• The terms remain the same

• The terms are multiplied

• The signs of the terms change

• The terms are added

What are the two equal factors of X^2 in the expression -X^2 + 49?

• X^2 and 49

• X and X

• X and 7

• 7 and 7

What are the two equal factors of 49 in the expression -X^2 + 49?

• 7 and 7

• X and X

• X^2 and 49

• 49 and 49

Why are the two factored forms of 49 - X^2 considered equivalent?

• They are not equivalent

• They have different signs

• They both simplify to the original expression

• They have different terms

What is the purpose of verifying the factored forms by multiplying them out?

• To simplify the expression

• To add complexity

• To ensure they equal the original expression

• To change the expression

What is the main takeaway from the video on factoring 49 - X^2?

• Different methods can yield equivalent results

• Only one method is correct

• Factoring is not possible

• The expression cannot be simplified