Simplifying Rational Expressions and Factors

The video tutorial explains how to multiply rational expressions by treating them like fractions. It emphasizes the importance of simplifying expressions by factoring out common elements before multiplying. Two examples are provided: the first involves prime factorization to simplify, while the second focuses on recognizing and simplifying common factors. The tutorial concludes with a reminder to avoid simplifying across addition or subtraction.

What is the first step in multiplying rational expressions?

• Multiply the numerators and denominators

• Add the numerators and denominators

• Divide the numerators by the denominators

• Subtract the numerators from the denominators

Why is it important to simplify common factors before multiplying?

• To make the expression longer

• To ensure the product is in simplest form

• To increase the number of terms

• To avoid using prime factorization

What is the prime factorization of 8x?

• 2 x 2 x 2 x x

• 3 x 3 x x

• 5 x 5 x x

• 2 x 3 x x

Which common factor is simplified first in the example?

• Five

• Y

• Two

• Three

What is the simplified product of the first example?

• 5x over 7z

• 2x over 9z

• 3x over 8z

• 4x over 6z

What should be done if a common factor is found in both the numerator and denominator?

• Add them together

• Divide them

• Multiply them

• Cancel them out

What is the result of simplifying 5y over 12z?

• 5y over 12z

• 5 over 12

• 1 over 12z

• 5 over z

What is the greatest common factor between 8 and 32 in the second example?

• 16

• 2

• 8

• 4

Why can't the x's be simplified in the second example?

• Because they are subtracted

• Because they are added

• Because they are multiplied

• Because they are in different terms

What is the simplified product of the second example?

• 3x over (x - 4)

• 4x over (x - 4)

• 5x over (x - 4)

• 2x over (x - 4)