Factoring and Simplifying Rational Expressions

The video tutorial explains how to simplify a given rational expression by factoring both the numerator and the denominator. It begins by factoring out the greatest common factor from the numerator, followed by applying the difference of squares formula to the denominator. The tutorial then identifies and cancels common factors between the numerator and denominator, resulting in a simplified expression.

What is the first step in simplifying a rational expression?

• Multiplying the numerator and denominator

• Factoring out the greatest common factor

• Dividing the numerator by the denominator

• Adding the numerator and denominator

What is the greatest common factor factored out from the numerator in this expression?

• X cubed

• a squared

• Y

• X squared

Which mathematical concept is used to factor the denominator in this expression?

• Difference of squares

• Binomial theorem

• Sum of cubes

• Quadratic formula

What are the factors of the denominator after applying the difference of squares formula?

• X cub - a^2 y and X cub + a^2 y

• X cub + a^2 y and X cub + a^2 y

• X cub - a^2 y and X cub - a^2 y

• X cub + a^2 y and X cub - a^2 y

What is the simplified form of the expression after canceling the common factor?

• X cubed divided by X cub - a^2 y

• X cubed divided by X cub + a^2 y

• X cubed times X cub - a^2 y

• X cubed times X cub + a^2 y