Multiplying and Simplifying Expressions

The video tutorial explains how to multiply monomials with binomials, emphasizing the importance of distribution and simplification. It provides two examples involving radicals, demonstrating the process of prime factorization and simplification of terms. The tutorial highlights the need to ensure that the final answer is simplified and shows how to handle terms with matching indexes.

What is the first step when multiplying a monomial by a binomial?

• Divide the monomial by each term in the binomial.

• Subtract the monomial from each term in the binomial.

• Add the monomial to each term in the binomial.

• Distribute the monomial across each term in the binomial.

In Example 1, what is the result of multiplying 5√10 by 2√6?

• 15√16

• 15√60

• 10√16

• 10√60

Why is it possible to multiply the terms in Example 1?

• Because the terms are all even numbers.

• Because the terms are all prime numbers.

• Because the indexes of the radicals match.

• Because the terms are all integers.

What is the importance of matching indexes in multiplication of radicals?

• It ensures the radicals can be multiplied.

• It ensures the radicals can be divided.

• It ensures the radicals can be added.

• It ensures the radicals can be subtracted.

What is the prime factorization of 60 in Example 1?

• 2^2 × 3^2 × 5

• 2 × 3 × 5^2

• 2 × 3^2 × 5

• 2^2 × 3 × 5

What is the process of rewriting a number using its prime factors called?

• Simplification

• Factorization

• Prime factorization

• Distribution

What is the result of dividing 150 by 5 in the prime factorization process?

• 30

• 15

• 10

• 25

In Example 1, what is the simplified form of 150?

• 2 × 3^2 × 5

• 2 × 3 × 5

• 2^2 × 3 × 5

• 2 × 3 × 5^2

What is the result of simplifying the expression in Example 1?

• 25√15 - 30

• 20√15 + 30

• 25√15 + 30

• 20√15 - 30

In Example 2, what is the result of multiplying 7√3 by 6?

• 42

• 42√3

• 18√3

• 18