By how much is `-12x + 2y` greater than the sum of ` -18x + 6y " and " 5x - 25 y`?

Options

A. `x + 21y`
B. `-x - 21y`
C. `x + 25y`
D. ` x + 36y`

Answer

To solve the problem, we need to find out how much the expression `-12x + 2y` is greater than the sum of the expressions `-18x + 6y` and `5x - 25y`. Let's break this down step by step.

### Step 1: Find the sum of the two expressions `-18x + 6y` and `5x - 25y`.

To do this, we will combine like terms:

\[ -18x + 6y + 5x - 25y \]

Combine the `x` terms:

\[ -18x + 5x = -13x \]

Now, combine the `y` terms:

\[ 6y - 25y = -19y \]

So, the sum of the two expressions is:

\[ -13x - 19y \]

### Step 2: Subtract the sum from the expression `-12x + 2y`.

Now we need to find out how much `-12x + 2y` is greater than `-13x - 19y`. This can be done by subtracting the sum from `-12x + 2y`:

\[ (-12x + 2y) - (-13x - 19y) \]

This simplifies to:

\[ -12x + 2y + 13x + 19y \]

### Step 3: Combine like terms again.

Now, combine the `x` terms:

\[ -12x + 13x = 1x \quad \text{or simply} \quad x \]

Next, combine the `y` terms:

\[ 2y + 19y = 21y \]

### Final Result:

Putting it all together, we get:

\[ x + 21y \]

Thus, `-12x + 2y` is greater than the sum of `-18x + 6y` and `5x - 25y` by the expression `x + 21y`.