Simplifying Expressions with the Distributive Property

The video tutorial introduces the distributive property as a method to simplify expressions, especially when variables or unlike terms are present inside parentheses. It explains the order of operations (PEMDAS) and how the distributive property helps in cases where direct simplification is not possible. The tutorial provides multiple examples and practice problems, demonstrating how to apply the distributive property and combine like terms. Advanced examples are also covered, offering a comprehensive understanding of the topic. The lesson concludes with a summary of key points and the importance of the distributive property in algebra.

What is the main purpose of the Distributive Property in simplifying expressions?

• To solve equations directly

• To eliminate parentheses when variables are involved

• To change the order of operations

• To combine like terms inside parentheses

In the Distributive Property formula a(b + c), what operation is performed between 'a' and 'b'?

• Division

• Addition

• Multiplication

• Subtraction

When using the Distributive Property, what should you do if the expression inside the parentheses involves subtraction?

• Only distribute to the first term

• Change the subtraction to addition

• Distribute the outside number to each term inside, keeping the subtraction sign

• Ignore the subtraction

What is the simplified form of 3(x + 6) using the Distributive Property?

• 3x + 6

• 3x + 18

• 3 + 6x

• 18x + 3

How do you handle a negative number outside the parentheses when using the Distributive Property?

• Only multiply the negative number with the first term

• Multiply the negative number with each term inside, keeping the sign

• Add the negative number to each term inside

• Ignore the negative sign

What is the result of distributing -1 to the expression (-7 + 3x)?

• -7 + 3x

• 7 - 3x

• -7 - 3x

• 7 + 3x

After distributing, what is the next step in simplifying an expression?

• Divide by the coefficient

• Solve for the variable

• Add all the terms

• Combine like terms

What is the simplified form of -6(5 + x) + 2(7x + 1)?

• -30 - 6x + 14x + 2

• -30 - 6x - 14x + 2

• -30 - 6x + 14x - 2

• -30 + 6x + 14x + 2

Why is the Distributive Property important when simplifying expressions with variables?

• It allows for the combination of like terms

• It changes the order of operations

• It eliminates parentheses, making further simplification possible

• It solves the equation directly

What is the final simplified form of the expression 2(3x - 4) - 5(x + 2)?

• 6x - 8 + 5x + 10

• 6x - 8 - 5x - 10

• 6x - 8 - 5x + 10

• 6x - 8 + 5x - 10