Factoring and the Distributive Property

The video tutorial explains the distributive property, which states that a factor multiplied by a sum is equal to multiplying that factor by each addend and then adding the products. It demonstrates how to factor expressions by identifying and extracting common factors, using examples like 3x + 3y and 18x + 27. The tutorial concludes by reinforcing the concept of factoring and checking the results by redistributing the factors.

What does the distributive property state?

• A factor multiplied by a sum is equal to the difference of the factor and each addend.

• A factor multiplied by a sum is equal to multiplying that factor by each addend and then adding the products.

• A factor multiplied by a sum is equal to the product of the factor and the sum.

• A factor multiplied by a sum is equal to the sum of the factor and each addend.

In the expression a(b + c), what does 'a' represent?

• An addend

• A product

• A sum

• A factor being distributed

What is the process of undoing distribution called?

• Factoring

• Subtracting

• Multiplying

• Adding

In the expression 3x + 3y, what is the common factor?

• x

• 3

• 6

• y

What is the factored form of 3x + 3y?

• 3(x + y)

• x(3 + y)

• y(3 + x)

• 3x + y

What is the common factor in the expression 18x + 27?

• 3

• 6

• 9

• 12

What is the factored form of 18x + 27?

• 27(0.67x + 1)

• 9(2x + 3)

• 18(x + 1.5)

• 3(6x + 9)

How can you verify the factored form of an expression?

• By subtracting the factors

• By adding the factors

• By dividing the factors

• By redistributing the factor

What is the result of redistributing 9 in the expression 9(2x + 3)?

• 18x + 27

• 9x + 3

• 2x + 3

• 18x + 3

What is the purpose of factoring in algebra?

• To subtract expressions

• To add expressions

• To complicate expressions

• To simplify expressions