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 best answer is B: − 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.
Combining xy Terms First, let's identify and combine the 'xy' terms. We have − 2 x y and − 2 x y . Combining these gives us: − 2 x y − 2 x y = − 4 x y
Combining x Terms Next, let's identify and combine the 'x' terms. We have 3 x and 3 x . Combining these gives us: 3 x + 3 x = 6 x
Simplified Expression Now, we write the simplified expression by combining the results from the previous steps: − 4 x y + 6 x
Selecting the Correct Option Comparing our simplified expression − 4 x y + 6 x with the given options, we see that it matches option B.
Examples
Simplifying expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are calculating the total cost of items with discounts and taxes, you often need to simplify the expression to find the final cost. Imagine you are buying 'x' number of apples and 'y' number of bananas. The cost of each apple is 3 dollars and the cost of each banana is 2 dollars. However, you have a discount of 2 dollars for every apple and banana you buy. The total cost can be expressed as 3 x + 2 y − 2 x − 2 y , which simplifies to x . This means the total cost only depends on the number of apples you buy after the discount.
