Understanding the Distributive Property and Greatest Common Factor

The video tutorial explains how to apply the distributive property to simplify expressions and how to factor out the greatest common factor. It begins with a basic introduction to the distributive property, followed by a detailed example of distributing 1/2 across the expression 2a-6b+8. The tutorial then shifts to factoring, demonstrating how to find and factor out the greatest common factor from the expression 60m-40. The video emphasizes understanding the process of distribution and factoring through examples and explanations.

What is the first step in applying the distributive property to the expression 1/2(2a-6b+8)?

• Subtract 6b from 2a.

• Divide each term by 2.

• Multiply 1/2 by each term inside the parentheses.

• Add all the terms together.

When applying the distributive property, what is the result of 1/2 times 2a?

• 4a

• a

• 1a

• 2a

What is the simplified form of the expression 1/2(2a-6b+8)?

• a-6b+8

• 2a-6b+8

• 2a-3b+4

• a-3b+4

What does it mean when terms are relatively prime?

• They have a common factor of two.

• They have no common factors other than one.

• They are both even numbers.

• They are both odd numbers.

What is the greatest common factor of 60m and 40?

• 30

• 20

• 5

• 10

How can you determine the greatest common factor using prime factorization?

• By adding all the prime factors together.

• By finding the highest power of each prime factor.

• By subtracting the smaller number from the larger number.

• By identifying the common prime factors and multiplying them.

What is the prime factorization of 60?

• 2 x 2 x 5

• 2 x 3 x 5

• 3 x 5 x 5

• 2 x 2 x 3 x 5

What is the result of factoring out the greatest common factor from 60m-40?

• 10(6m-4)

• 30(2m-1)

• 20(3m-2)

• 5(12m-8)

Why is 20 considered the greatest common factor of 60m and 40?

• Because it is the sum of the two numbers.

• Because it is a prime number.

• Because it is the smallest number that divides both terms.

• Because it is the largest number that divides both terms.

What is the significance of ensuring that the terms left after factoring are relatively prime?

• It ensures the factorization is complete.

• It makes the expression easier to add.

• It ensures the terms are equal.

• It allows for further simplification.