Simplify.
$6 a^2-2 c+2 a^2-2 c^2$
Answer (1)
Combine like terms: 6 a 2 + 2 a 2 = 8 a 2 .
Rewrite the expression: 8 a 2 − 2 c − 2 c 2 .
The simplified expression is 8 a 2 − 2 c 2 − 2 c .
Explanation
Understanding the Problem We are asked to simplify the expression 6 a 2 − 2 c + 2 a 2 − 2 c 2 . This involves combining like terms.
Combining Like Terms The like terms in the expression are 6 a 2 and 2 a 2 . Combining these gives us 6 a 2 + 2 a 2 = 8 a 2 .
Rewriting the Expression Now we rewrite the expression with the combined like terms: 8 a 2 − 2 c − 2 c 2 .
Final Answer The simplified expression is 8 a 2 − 2 c − 2 c 2 .
Examples
Simplifying expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are calculating the area of a room and have expressions for the length and width that can be simplified, doing so will make the calculation easier. Also, in computer programming, simplifying expressions can optimize code and make it run faster. Understanding how to combine like terms and simplify expressions is crucial for success in higher-level math and science courses.
