`(3q + 7 p^(2) - 2r^(3) + 4) - (4 p^(2) - 2q + 7r^(3) - 3) = ?`

Options

A. `(p^(2) + 2q + 5r^(3) + 1)`
B. `(11p^(2) + q + 5r^(3) + 1)`
C. `(-3p^(2) - 5q + 9r^(3) - 7)`
D. `(3 p^(2) + 5q - 9r^(3) + 7)`

Answer

To solve the expression \((3q + 7p^2 - 2r^3 + 4) - (4p^2 - 2q + 7r^3 - 3)\), we will follow these steps:

### Step 1: Distribute the negative sign
The expression can be rewritten by distributing the negative sign across the second set of parentheses. This means changing the signs of each term inside the parentheses:

\[ (3q + 7p^2 - 2r^3 + 4) - (4p^2 - 2q + 7r^3 - 3) = 3q + 7p^2 - 2r^3 + 4 - 4p^2 + 2q - 7r^3 + 3 \]

### Step 2: Combine like terms
Now, we will combine the like terms from the expression:

- For \(q\) terms: \(3q + 2q = 5q\)
- For \(p^2\) terms: \(7p^2 - 4p^2 = 3p^2\)
- For \(r^3\) terms: \(-2r^3 - 7r^3 = -9r^3\)
- For constant terms: \(4 + 3 = 7\)

Putting it all together, we have:

\[ 5q + 3p^2 - 9r^3 + 7 \]

### Final Answer
Thus, the final simplified expression is:

\[ 5q + 3p^2 - 9r^3 + 7 \]

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