Simplify $-2xy + 3x - 2xy + 3x$
A) $-4xy + 6x$
B) $4xy + 6x$
C) $4xy - 6x$
D) $2xy$
Answer (1)
Combine the 'xy' terms: − 2 x y − 2 x y = − 4 x y .
Combine the 'x' terms: 3 x + 3 x = 6 x .
Write the simplified expression: − 4 x y + 6 x .
The correct answer is: − 4 x y + 6 x .
Explanation
Understanding the Expression We are asked to simplify the expression − 2 x y + 3 x − 2 x y + 3 x . This involves combining like terms, which are terms that have the same variables raised to the same powers.
Identifying Like Terms First, let's identify the like terms. We have two terms with x y : − 2 x y and − 2 x y . We also have two terms with x : 3 x and 3 x .
Combining Like Terms Now, let's combine the x y terms: − 2 x y − 2 x y = − 4 x y Next, let's combine the x terms: 3 x + 3 x = 6 x
Simplified Expression So, the simplified expression is − 4 x y + 6 x . Now we compare this with the given choices.
Final Answer The simplified expression − 4 x y + 6 x matches option A. Therefore, the correct answer is A) − 4 x y + 6 x .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics and has numerous real-world applications. For example, imagine you are calculating the total cost of items you are purchasing. If you buy 'x' number of apples at a price of 3 dollars each and 'y' number of bananas at a price of 2 dollars each, and then you buy the same amount of apples and bananas again, the total cost can be represented as 3 x + 2 y + 3 x + 2 y . Simplifying this expression gives 6 x + 4 y , which makes it easier to calculate the total cost for any number of apples and bananas.
