Subtract :
`4x^(2)-3x+4" from "8x^(2)-5x-8`

Answer

To solve the problem of subtracting \( 4x^2 - 3x + 4 \) from \( 8x^2 - 5x - 8 \), we will follow these steps:

### Step 1: Write the expression to be subtracted
We start with the expression we want to subtract from, which is:
\[ 8x^2 - 5x - 8 \]
Next, we need to subtract the expression \( 4x^2 - 3x + 4 \) from it. This can be written as:
\[ 8x^2 - 5x - 8 - (4x^2 - 3x + 4) \]

### Step 2: Distribute the negative sign
Now, we will distribute the negative sign across the second expression:
\[ 8x^2 - 5x - 8 - 4x^2 + 3x - 4 \]

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

Putting it all together, we have:
\[ 4x^2 - 2x - 12 \]

### Step 4: Factor if possible
We can factor out a common factor from the expression:
\[ 4x^2 - 2x - 12 = 2(2x^2 - x - 6) \]

Thus, the final answer is:
\[ 2(2x^2 - x - 6) \]

### Final Answer:
\[ 2(2x^2 - x - 6) \]

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