Simplify: $4 x-2(4 x-2)$
Answer (1)
Distribute the -2 into the parenthesis: − 2 ( 4 x − 2 ) = − 8 x + 4 .
Rewrite the expression: 4 x − 8 x + 4 .
Combine like terms: ( 4 x − 8 x ) + 4 = − 4 x + 4 .
The simplified expression is − 4 x + 4 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 x − 2 ( 4 x − 2 ) . This involves distributing the − 2 across the terms inside the parenthesis and then combining like terms.
Distributing the -2 First, we distribute the − 2 to both terms inside the parenthesis: − 2 ( 4 x − 2 ) = − 2 × 4 x − 2 × ( − 2 ) = − 8 x + 4
Substituting Back Now, we substitute this back into the original expression: 4 x − 2 ( 4 x − 2 ) = 4 x − 8 x + 4
Combining Like Terms Next, we combine the like terms, which are the terms with x : 4 x − 8 x = ( 4 − 8 ) x = − 4 x
Final Simplified Expression Finally, we write the simplified expression: − 4 x + 4
Examples
Simplifying algebraic expressions is a fundamental skill in algebra and is used in many real-world applications. For example, suppose you are buying concert tickets online. The price of each ticket is x , and there is a service fee of $2 per ticket. You are buying 4 tickets, but you have a coupon that gives you a $2 discount on the total cost. The total cost can be expressed as 4 ( x + 2 ) − 2 ( 4 ) . Simplifying this expression gives 4 x + 8 − 8 = 4 x . This means the total cost is simply 4 times the price of each ticket. This type of simplification helps in understanding costs, profits, and other financial calculations.
