Distributive Property and Like Terms

This video tutorial explains how to simplify algebraic expressions using the distributive property. It begins with an introduction to the property, explaining how a number outside parentheses can be distributed to terms inside. The video then provides two examples: one with numbers and another with variables, demonstrating the process of distributing and simplifying expressions. The tutorial emphasizes that terms cannot be combined unless they are like terms, and highlights the importance of matching exponents when dealing with variables.

What is the main purpose of the distributive property in algebra?

• To subtract numbers

• To multiply a single term across terms inside parentheses

• To divide numbers

• To add numbers

Which of the following expressions correctly uses the distributive property?

• a(b + c) = a(bc)

• a(b + c) = ab - ac

• a(b + c) = a + b + c

• a(b + c) = ab + ac

What is the first step in using the distributive property?

• Divide all terms

• Subtract all terms

• Add all terms

• Multiply the term outside the parentheses by each term inside

In the expression a(b + c), what does the distributive property allow you to do?

• Multiply a by b and c separately

• Add a to b and c

• Subtract a from b and c

• Divide a by b and c

What is one advantage of using the distributive property?

• It is only useful for addition

• It helps in clearing parentheses

• It makes expressions longer

• It complicates calculations

In the expression -2(5x - 4y + 3), what is the result of distributing -2 to 5x?

• 5x

• -10x

• 10x

• -5x

What is the result of distributing -2 to -4y in the expression -2(5x - 4y + 3)?

• -8y

• 4y

• 8y

• -4y

Why can't the terms -10x, 8y, and -6 be combined in the expression -10x + 8y - 6?

• They are not like terms

• They are like terms

• They are all variables

• They are all constants

What is the result of multiplying -2 by 3 in the expression -2(5x - 4y + 3)?

• -6

• 3

• 6

• -3

In the expression 4x(7x^2 - 6x + 1), what is the result of distributing 4x to 7x^2?

• 7x^2

• 7x^3

• 28x^2

• 28x^3