Subtract `5x^2 - 4y^2 + 6y - 3` from `7x^2 - 4xy + 8y^2 + 5x - 3y`.

Explanation

To subtract the polynomial \(5x^2 - 4y^2 + 6y - 3\) from \(7x^2 - 4xy + 8y^2 + 5x - 3y\), we follow these steps:

### Step 1: Write down the expression
We need to subtract the first polynomial from the second polynomial:
\[ (7x^2 - 4xy + 8y^2 + 5x - 3y) - (5x^2 - 4y^2 + 6y - 3) \]

### Step 2: Distribute the negative sign
When we subtract the second polynomial, we need to distribute the negative sign across all terms:
\[ 7x^2 - 4xy + 8y^2 + 5x - 3y - 5x^2 + 4y^2 - 6y + 3 \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- For \(x^2\) terms: \(7x^2 - 5x^2 = 2x^2\)
- For \(xy\) terms: \(-4xy\) (there are no other \(xy\) terms)
- For \(y^2\) terms: \(8y^2 + 4y^2 = 12y^2\)
- For \(x\) terms: \(5x\) (there are no other \(x\) terms)
- For \(y\) terms: \(-3y - 6y = -9y\)
- For constant terms: \(-3 + 3 = 0\)

Putting it all together, we get:
\[ 2x^2 - 4xy + 12y^2 + 5x - 9y \]

### Final Answer:
Thus, the result of the subtraction is:
\[ 2x^2 - 4xy + 12y^2 + 5x - 9y \]

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