Simplifying Expressions and Factors

The video tutorial explains how to multiply rational expressions by first simplifying them. It emphasizes the importance of factoring numerators and denominators to identify common factors. Two examples are provided to illustrate the process of factoring and simplifying rational expressions, highlighting the need to avoid simplifying across addition or subtraction. The tutorial concludes with a reminder to leave products in factored form.

Why is it important to simplify common factors before multiplying rational expressions?

• To avoid using prime factorization

• To increase the number of terms

• To ensure the final product is in simplest form

• To make the expressions more complex

In the first example, why can't 2x and 4x be simplified?

• Because they are not monomials

• Because they involve addition or subtraction

• Because they are already in simplest form

• Because they are not prime numbers

What is the prime factorization of 15?

• 2 x 7.5

• 3 x 5

• 15 x 1

• 5 x 3

What is the greatest common factor of 4 and 6?

• 1

• 2

• 3

• 4

Why can't the x terms be simplified in the first example?

• Because they are part of a subtraction

• Because they are not in factored form

• Because they are not common factors

• Because they are already simplified

In the second example, what is the greatest common factor of x^2 + x?

• x

• x + 1

• 1

• x^2

What is the common factor of 5x + 10 in the second example?

• 10

• 2

• x

• 5

Why is it important to leave the product in factored form?

• To avoid errors in addition

• To make it more complex

• To ensure it is in simplest form

• To make it easier to multiply again

What happens to the factor of x + 1 in the second example?

• It is multiplied by 2

• It is simplified to 1

• It is added to the denominator

• It is left unchanged

What is the final form of the numerator in the second example?

• x^2

• x + 2

• 5x

• 2x