Exploring the Distributive Property with Area Models

This video tutorial introduces the distributive property using an area model. It explains how to distribute terms across expressions, starting with positive numbers, then negative numbers, and finally variables. The tutorial includes several examples and concludes with challenge problems to test understanding. The video emphasizes the connection between real-world distribution and mathematical distribution, providing a comprehensive understanding of the concept.

What does the distributive property allow us to do in mathematics?

• Subtract each term inside the parentheses from the number outside.

• Add all numbers inside and outside the parentheses.

• Multiply a number outside the parentheses to each term inside.

• Divide a number by a sum or difference inside parentheses.

What real-world concept is similar to distributing in mathematics?

• Collecting goods from different centers.

• Storing goods in a warehouse.

• Dealing out or distributing goods from a center.

• Buying goods from a supermarket.

How do we use the area model to distribute 2(b + 3)?

• 2b + 3

• 2b + 6

• b + 6

• 4b + 6

What is the result of distributing -2(b + 3) using the area model?

• -2b - 6

• -2b + 6

• 2b - 6

• -4b - 6

When multiplying two negatives, the result is:

• Undefined

• Zero

• Always positive

• Always negative

What is the simplified form of x(3x + 1)?

• 4x^2

• 3x^2 + x

• 3x + x

• 3x^2 + 1

How do we simplify the expression j^2(-8j + 4)?

• -8j^3 + 4j^2

• -8j^2 + 4j

• 8j^3 + 4

• -8j + 4j^2

What is the result of distributing b(4 + 5)?

• 20b

• 9b

• 4b + 5b

• b + 9

What does the expression 2i(-3y + 9) simplify to?

• -6y^2 + 18i

• -6iy^2 + 18y

• -6iy + 18i

• -6y^2 + 18iy

After distributing and combining like terms, what is the simplified form of -1/2a^2(4a - a^2 + 10a + 6 - 8)?

• -1/2a^4 - 7a^3 - a^2

• 1/2a^4 - 7a^3 + a^2

• 1/2a^4 + 7a^3 + a^2

• -1/2a^4 + 7a^3 - a^2