`A=2x+3xy+7x^(2),B=3x-2xy-5x^(2) and C=2xy-6x^(2)-3x`. Find the value of A+B-C.

Explanation

To find the value of A + B - C, we will first substitute the values of A, B, and C and then perform the operations step by step.

Given:
- \( A = 2x + 3xy + 7x^2 \)
- \( B = 3x - 2xy - 5x^2 \)
- \( C = 2xy - 6x^2 - 3x \)

### Step 1: Write the expression for A + B - C
We need to calculate:
\[ A + B - C = (2x + 3xy + 7x^2) + (3x - 2xy - 5x^2) - (2xy - 6x^2 - 3x) \]

### Step 2: Combine A and B
Combine the expressions for A and B:
\[ A + B = (2x + 3xy + 7x^2) + (3x - 2xy - 5x^2) \]

### Step 3: Combine like terms in A + B
Now, we will combine the like terms:
- For the \(x\) terms: \(2x + 3x = 5x\)
- For the \(xy\) terms: \(3xy - 2xy = xy\)
- For the \(x^2\) terms: \(7x^2 - 5x^2 = 2x^2\)

So,
\[ A + B = 5x + xy + 2x^2 \]

### Step 4: Substitute C and change the signs
Now, we will substitute C into the expression and change the signs:
\[ -C = -(2xy - 6x^2 - 3x) = -2xy + 6x^2 + 3x \]

### Step 5: Combine A + B with -C
Now we will combine \(A + B\) with \(-C\):
\[ A + B - C = (5x + xy + 2x^2) + (-2xy + 6x^2 + 3x) \]

### Step 6: Combine like terms
Now, we will combine the like terms:
- For the \(x\) terms: \(5x + 3x = 8x\)
- For the \(xy\) terms: \(xy - 2xy = -xy\)
- For the \(x^2\) terms: \(2x^2 + 6x^2 = 8x^2\)

So, the final expression is:
\[ A + B - C = 8x - xy + 8x^2 \]

### Final Answer
Thus, the value of \( A + B - C \) is:
\[ 8x - xy + 8x^2 \]

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