Identifying Equivalent Mathematical Expressions with Variables

Front

What is an equivalent expression?

Back

An equivalent expression is an expression that has the same value as another expression, even if it looks different.

Front

What does it mean to combine like terms?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you simplify the expression 3x + 5x?

Back

You combine like terms to get 8x.

Front

What is the result of applying the distributive property to 4(2x + 3)?

Back

The result is 8x + 12.

Front

Is the expression 2(x + 4) equivalent to 2x + 8?

Back

Yes, because applying the distributive property gives you 2x + 8.

Front

What is the first step in simplifying the expression 5a + 3a - 2?

Back

Combine like terms to get 8a - 2.

Front

How can you express 12y + 8y using the distributive property?

Back

You can express it as 4(3y + 2y).

Front

What does it mean for two expressions to be equivalent?

Back

It means they have the same value for all values of the variables involved.

Front

How do you check if 6x - 3 is equivalent to 3(2x - 1)?

Back

Use the distributive property on 3(2x - 1) to get 6x - 3, confirming they are equivalent.