Add : `3x^(2)+5x-4, 2x+3-x^(2) and 8-3x+7x^(2)`.

Answer

To solve the problem of adding the three algebraic expressions \(3x^2 + 5x - 4\), \(2x + 3 - x^2\), and \(8 - 3x + 7x^2\), we will follow these steps:

### Step 1: Write down the expressions
We have three expressions to add:
1. \(3x^2 + 5x - 4\)
2. \(2x + 3 - x^2\)
3. \(8 - 3x + 7x^2\)

### Step 2: Rearrange the expressions
To make it easier to add, we will rearrange the terms in each expression in descending order of the power of \(x\):
- The first expression remains as \(3x^2 + 5x - 4\).
- The second expression can be rearranged to \(-x^2 + 2x + 3\).
- The third expression can be rearranged to \(7x^2 - 3x + 8\).

So, we have:
\[ 3x^2 + 5x - 4, \quad -x^2 + 2x + 3, \quad 7x^2 - 3x + 8 \]

### Step 3: Combine like terms
Now, we will combine the like terms from all three expressions.

**Combine \(x^2\) terms:**
\[ 3x^2 - x^2 + 7x^2 = (3 - 1 + 7)x^2 = 9x^2 \]

**Combine \(x\) terms:**
\[ 5x + 2x - 3x = (5 + 2 - 3)x = 4x \]

**Combine constant terms:**
\[ -4 + 3 + 8 = (-4 + 3 + 8) = 7 \]

### Step 4: Write the final result
Putting it all together, we get:
\[ 9x^2 + 4x + 7 \]

### Final Answer:
The sum of the three expressions is:
\[ \boxed{9x^2 + 4x + 7} \]