Take away `-3x^(3) + 4x^(2) - 5x + 6` from `3x^(3) - 4x^(2) + 5x - 6`

Answer

To solve the problem of taking away \(-3x^3 + 4x^2 - 5x + 6\) from \(3x^3 - 4x^2 + 5x - 6\), we will perform the following steps:

### Step 1: Write the expression for subtraction
We need to subtract the polynomial \(-3x^3 + 4x^2 - 5x + 6\) from \(3x^3 - 4x^2 + 5x - 6\). This can be expressed as:
\[ (3x^3 - 4x^2 + 5x - 6) - (-3x^3 + 4x^2 - 5x + 6) \]

### Step 2: Change the signs of the second polynomial
When we subtract a polynomial, we can change the signs of all the terms in the polynomial being subtracted:
\[ = 3x^3 - 4x^2 + 5x - 6 + 3x^3 - 4x^2 + 5x - 6 \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- For \(x^3\) terms: \(3x^3 + 3x^3 = 6x^3\)
- For \(x^2\) terms: \(-4x^2 - 4x^2 = -8x^2\)
- For \(x\) terms: \(5x + 5x = 10x\)
- For constant terms: \(-6 - 6 = -12\)

Putting it all together, we have:
\[ 6x^3 - 8x^2 + 10x - 12 \]

### Final Answer:
Thus, the result of taking away \(-3x^3 + 4x^2 - 5x + 6\) from \(3x^3 - 4x^2 + 5x - 6\) is:
\[ \boxed{6x^3 - 8x^2 + 10x - 12} \]