Distributive Property

The video tutorial explains the distributive property, demonstrating how to simplify expressions with variables and real numbers. It provides examples and practice problems to reinforce understanding, concluding with a review of key concepts.

What is the distributive property in algebra?

• a * (b + c) = a * b + a * c

• a + b = b + a

• a * b = b * a

• a - b = b - a

How can the distributive property be applied to the expression 4 * (2 + 1)?

• 4 + 2 * 1

• 4 * 2 * 1

• 4 + 2 + 1

• 4 * 2 + 4 * 1

When using the distributive property on 4x * (2x + y), what is the result?

• 4x^2 + y

• 8x^2 + 4xy

• 4x^2 + 2xy

• 8x + 4y

In the expression -3 * (3a^2 - 8a + 7), what is the result after applying the distributive property?

• -9a^2 + 24a - 21

• -9a^2 - 24a + 21

• 9a^2 - 24a + 21

• 9a^2 + 24a - 21

How do you simplify 2xy * (x^2 - 3xy + 4y) using the distributive property?

• 2x^3y - 6x^2y^2 + 8xy^2

• 2x^3y + 6x^2y^2 - 8xy^2

• 2x^3y - 6xy^2 + 8x^2y

• 2x^3y + 6xy^2 - 8x^2y

What is the result of applying the distributive property to x/6 * (x^2 + 5x - 9)?

• x^3/6 + 5x^2/6 - 9x/6

• x^3/6 + 5x/6 - 9/6

• x^3/6 + 5x^2/6 + 9x/6

• x^3/6 - 5x^2/6 + 9x/6

What is a helpful strategy when applying the distributive property to complex expressions?

• Draw lines to each term and rewrite the expression

• Add all terms together first

• Multiply only the first and last terms

• Ignore the coefficients

How do you simplify 5y * (3x - 2) using the distributive property?

• 5y - 6x

• 15y - 10x

• 15yx - 10y

• 5x - 10y

What is the result of applying the distributive property to 4 * (a^2b - 6ab^2 - 2b^3)?

• 4a^2b - 24ab^2 - 8b^3

• 4a^2b + 24ab^2 + 8b^3

• 4a^2b - 24ab^2 + 8b^3

• 4a^2b + 24ab^2 - 8b^3

What is the simplified form of 1/4 * (7x^2 - 4x + 8) using the distributive property?

• 7x^2/4 + x/4 - 2

• 7x^2/4 - x/4 + 2

• 7x^2/4 - x + 2

• 7x^2/4 + x - 2