Understanding the Distributive Property

The video tutorial explains the distributive property, a key concept in mathematics. It begins with an introduction to the success criteria for understanding the property, followed by a detailed explanation of the key idea: multiplying a sum or difference by a number involves multiplying each term inside the parentheses by the number outside. The tutorial provides two examples: a numerical example using specific numbers and an algebraic example using variables. These examples illustrate how to apply the distributive property step-by-step, emphasizing the importance of multiplying each term and simplifying the result.

What is the main idea behind the distributive property?

• To subtract the number inside from the number outside.

• To add numbers inside the parentheses first.

• To divide the number outside by the sum inside.

• To multiply each term inside the parentheses by the number outside.

In the example 3(7 + 2), what is the result of applying the distributive property?

• 21 + 2

• 3 + 14

• 21 + 6

• 7 + 6

What is the final simplified result of 3(7 + 2) using the distributive property?

• 23

• 27

• 21

• 19

In algebraic terms, how do you express the distributive property for a(b + c)?

• ab + ac

• a + b + c

• b + ac

• a(bc)

What is the first step in applying the distributive property to a(b + c)?

• Subtract b from c.

• Multiply a by c.

• Multiply a by b.

• Add b and c.

Why can't you combine ab and ac further in the expression a(b + c)?

• They are different operations.

• They are constants.

• They are already simplified.

• They are not like terms.

What operation must be brought down when applying the distributive property?

• Subtraction

• Multiplication

• Addition

• Division

What is the result of applying the distributive property to 4(x + 5)?

• 4 + 5x

• 4x + 5

• x + 20

• 4x + 20

What is the purpose of the distributive property in mathematics?

• To calculate the area of a rectangle.

• To solve equations by isolating variables.

• To find the greatest common factor.

• To simplify expressions by distributing multiplication over addition or subtraction.