Evaluating and Simplifying Expressions

The video tutorial guides students through simplifying and evaluating algebraic expressions. It begins with an introduction to the problem, followed by step-by-step simplification of two expressions. The tutorial demonstrates how to evaluate both the original and simplified expressions for given variable values, ensuring they are equivalent. The process involves distributing terms, combining like terms, and following the order of operations. The video concludes by confirming the equivalence of the expressions and summarizing the key steps.

What is the main task in this activity?

• To graph functions

• To find the derivative

• To simplify and evaluate expressions

• To solve equations

What operation is performed to clear the parentheses in the first expression?

• Division

• Addition

• Subtraction

• Distribution

What is the simplified form of the expression 5w - 2(4 - 2w)?

• 3w + 2

• 9w - 8

• 5w + 4

• 7w - 8

When evaluating the original expression for w = -2, what is the result?

• -18

• -10

• -8

• -26

Why should the original and simplified expressions yield the same result?

• Because they are different

• Because they are equivalent

• Because they are opposites

• Because they are unrelated

What is the first step in simplifying the second example?

• Factor the expression

• Divide by a constant

• Combine like terms

• Clear parentheses

What are the like terms in the expression 3xy + 4xy - 6x - 2x?

• 3xy and 4xy

• 4xy and -2x

• 3xy and -6x

• -6x and -2x

What is the simplified form of the expression 3xy + 4xy - 6x - 2x?

• 6xy - 6x

• 8xy - 10x

• 5xy - 4x

• 7xy - 8x

What is the result of evaluating the simplified expression for x = 3 and y = -1?

• -27

• -39

• -33

• -45

Why do both expressions in the second example yield the same result?

• They are different

• They are equivalent

• They are opposites

• They are unrelated