If `A =3x^(2) -4x +1, B =5x^(2) + 3x-8` and `C = 4x^(2) - 7x + 3`, then find (A+B)-C.

Answer

To solve the expression \((A + B) - C\) where:

- \(A = 3x^2 - 4x + 1\)
- \(B = 5x^2 + 3x - 8\)
- \(C = 4x^2 - 7x + 3\)

we will follow these steps:

### Step 1: Add \(A\) and \(B\)

First, we need to find \(A + B\):

\[ A + B = (3x^2 - 4x + 1) + (5x^2 + 3x - 8) \]

Combine like terms:

- Combine \(x^2\) terms: \(3x^2 + 5x^2 = 8x^2\)
- Combine \(x\) terms: \(-4x + 3x = -x\)
- Combine constant terms: \(1 - 8 = -7\)

So,

\[ A + B = 8x^2 - x - 7 \]

### Step 2: Subtract \(C\) from \(A + B\)

Now, we need to subtract \(C\) from \(A + B\):

\[ (A + B) - C = (8x^2 - x - 7) - (4x^2 - 7x + 3) \]

Distributing the negative sign:

\[ = 8x^2 - x - 7 - 4x^2 + 7x - 3 \]

### Step 3: Combine like terms

Now, combine the like terms:

- Combine \(x^2\) terms: \(8x^2 - 4x^2 = 4x^2\)
- Combine \(x\) terms: \(-x + 7x = 6x\)
- Combine constant terms: \(-7 - 3 = -10\)

So,

\[ (A + B) - C = 4x^2 + 6x - 10 \]

### Final Answer

Thus, the final result is:

\[ (A + B) - C = 4x^2 + 6x - 10 \]

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