Add the following : `2x^2y`,`-4x^2y`,`6x^2y`,`-5x^2y`

Options

A. `x^2y`
B. `-x^2y`
C. `17x^2y`
D. `15x^2y`

Answer

To solve the problem of adding the algebraic expressions \(2x^2y\), \(-4x^2y\), \(6x^2y\), and \(-5x^2y\), we can follow these steps:

### Step 1: Write down the expressions
We start with the expressions:
\[ 2x^2y, \quad -4x^2y, \quad 6x^2y, \quad -5x^2y \]

### Step 2: Combine the expressions
We can combine these expressions by adding them together:
\[ 2x^2y + (-4x^2y) + 6x^2y + (-5x^2y) \]

### Step 3: Group the like terms
Since all the terms have the common factor \(x^2y\), we can factor it out:
\[ = x^2y \left(2 + (-4) + 6 + (-5)\right) \]

### Step 4: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ = x^2y \left(2 - 4 + 6 - 5\right) \]

Calculating step-by-step:
1. \(2 - 4 = -2\)
2. \(-2 + 6 = 4\)
3. \(4 - 5 = -1\)

So we have:
\[ = x^2y \cdot (-1) \]

### Step 5: Write the final answer
Thus, the final result is:
\[ -1x^2y \quad \text{or simply} \quad -x^2y \]

### Summary of the steps:
1. Write down the expressions.
2. Combine the expressions.
3. Group the like terms.
4. Simplify the expression inside the parentheses.
5. Write the final answer.

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