3.9 Identifying Equivalent Expressions

Front

What is an equivalent expression?

Back

An equivalent expression is an expression that has the same value as another expression for all values of the variable(s) involved.

Front

How do you simplify the expression 7(2g - 2)?

Back

To simplify, distribute the 7: 7 * 2g - 7 * 2 = 14g - 14.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

If 3(x + 4) = 3x + 12, what property is being used?

Back

The distributive property is being used to expand the expression.

Front

What does it mean to factor an expression?

Back

Factoring an expression means to express it as a product of its factors, often simplifying the expression.

Front

How can you check if two expressions are equivalent?

Back

You can check if two expressions are equivalent by substituting the same value for the variable(s) in both expressions and seeing if they yield the same result.

Front

What is the result of combining like terms in the expression 5x + 3x - 2?

Back

The result is 8x - 2.

Front

What is the first step in simplifying the expression 4(3y + 2) - 5?

Back

The first step is to distribute the 4: 4 * 3y + 4 * 2 - 5 = 12y + 8 - 5.

Front

What is the purpose of using parentheses in expressions?

Back

Parentheses indicate which operations should be performed first in an expression, following the order of operations.

Front

How do you identify like terms in an expression?

Back

Like terms are terms that have the same variable raised to the same power, such as 2x and 5x.