Exploring the Distributive Property in Multiplication and Addition

What does the distributive property of multiplication over addition state?

• You add the numbers inside the parentheses first.

• You divide each term inside the parentheses by the number outside.

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

• You subtract the numbers inside the parentheses first.

In the example 4 * (2 + 3), what is the result after applying the distributive property?

• 4 * 2 + 3

• 4 + 2 * 3

• 4 * (2 + 3)

• 4 * 2 + 4 * 3

Why might we use the distributive property instead of just adding the numbers inside the parentheses first?

• It always gives a different result.

• It is required by the order of operations.

• It helps when dealing with variables.

• It makes the calculation faster.

What is the result of 4 * (x + y) using the distributive property?

• 4x + y

• x + 4y

• 4 + xy

• 4x + 4y

If x = 2 and y = 3, what is the value of 4 * (x + y) after applying the distributive property?

• 14

• 8

• 20

• 12

What is factoring in relation to the distributive property?

• Multiplying each term by a common factor.

• Adding terms together.

• Reversing the distributive property to factor out a common term.

• Dividing each term by a common factor.

In the expression 3x + 3y, what is the common factor that can be factored out?

• xy

• x

• y

• 3

What is the result of factoring out 3 from the expression 3x + 3y?

• 3(xy)

• x + y

• 3(x + y)

• 3x + y

What happens if you apply the distributive property to the factored expression 3(x + y)?

• You get 3xy

• You get x + y

• You get 3x + 3y

• You get 3x + y

Why is it important to learn both the distributive property and factoring?

• They are only used in advanced mathematics.

• They are used in geometry.

• They help in simplifying and solving algebraic expressions.

• They are both required for all math problems.