Equivalent Expressions

Front

What are equivalent expressions?

Back

Equivalent expressions are expressions that have the same value for all values of the variable(s) involved.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute the multiplication over addition.

Front

True or False: 5(2 + 1) = 5(2) + 1

Back

False. The correct application of the distributive property gives 5(2 + 1) = 5*2 + 5*1 = 10 + 5 = 15.

Front

How do you simplify the expression 12(3 + 4)?

Back

You apply the distributive property: 12(3 + 4) = 12*3 + 12*4 = 36 + 48.

Front

What is the result of 5(3 + 2)?

Back

Using the distributive property, 5(3 + 2) = 5*3 + 5*2 = 15 + 10 = 25.

Front

True or False: 4(5) = 45

Back

False. 4(5) = 20, not 45.

Front

What is the result of the expression 8(x + 5)?

Back

Using the distributive property, 8(x + 5) = 8x + 40.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they yield the same result when evaluated for the same value of the variable.

Front

What is the first step in simplifying an expression using the distributive property?

Back

The first step is to multiply the term outside the parentheses by each term inside the parentheses.

Front

Can you give an example of equivalent expressions?

Back

Yes, 2(x + 3) and 2x + 6 are equivalent expressions.