Subtract polynomial from another polynomial

1. Identify the polynomials: The problem asks to subtract the polynomial $-2x^2 + 2$ from the polynomial $-3x^2 + 10$.
2. Set up the subtraction: When subtracting one expression from another, the expression being subtracted is placed after the minus sign. So, we write this as:
$$(-3x^2 + 10) - (-2x^2 + 2)$$
3. Distribute the negative sign: The negative sign in front of the second parenthesis applies to each term inside it. This means we change the sign of each term in the second polynomial.
$$ -3x^2 + 10 + 2x^2 - 2$$
4. Group like terms: Combine the terms with the same variable and exponent. In this case, we group the $x^2$ terms and the constant terms.
$$( -3x^2 + 2x^2 ) + ( 10 - 2 )$$
5. Combine like terms: Perform the addition and subtraction for each group.
$$-x^2 + 8$$
6. State the final answer: The result of subtracting $-2x^2 + 2$ from $-3x^2 + 10$ is $-x^2 + 8$.