Subtract : `5x - 3x^(2) + 8xy` from `7x^(2) + 3xy - 4x`.

Answer

To solve the problem of subtracting \(5x - 3x^2 + 8xy\) from \(7x^2 + 3xy - 4x\), we will follow these steps:

### Step 1: Write the expression for subtraction
We start with the expression:
\[ 7x^2 + 3xy - 4x - (5x - 3x^2 + 8xy) \]

### Step 2: Distribute the negative sign
Next, we distribute the negative sign across the second expression:
\[ 7x^2 + 3xy - 4x - 5x + 3x^2 - 8xy \]

### Step 3: Combine like terms
Now, we will combine the like terms. We will group the \(x^2\) terms, \(xy\) terms, and \(x\) terms separately:
- \(x^2\) terms: \(7x^2 + 3x^2\)
- \(xy\) terms: \(3xy - 8xy\)
- \(x\) terms: \(-4x - 5x\)

Calculating each group:
- \(7x^2 + 3x^2 = 10x^2\)
- \(3xy - 8xy = -5xy\)
- \(-4x - 5x = -9x\)

### Step 4: Write the final expression
Combining all the simplified terms, we get:
\[ 10x^2 - 5xy - 9x \]

Thus, the final answer is:
\[ 10x^2 - 5xy - 9x \]

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