Subtract a polynomial from another polynomial

1. Identify the polynomials: The problem asks to subtract the polynomial $6x^2 - 7x - 2$ from the polynomial $6x^2 - 2x + 6$. The first polynomial is the subtrahend, and the second is the minuend.
2. Set up the subtraction: To subtract one polynomial from another, we write the minuend and then subtract the subtrahend. This can be written as: $(6x^2 - 2x + 6) - (6x^2 - 7x - 2)$.
3. Distribute the negative sign: When subtracting a polynomial, we distribute the negative sign to each term within the parentheses of the subtrahend. This changes the sign of each term in the subtrahend: $6x^2 - 2x + 6 - 6x^2 + 7x + 2$.
4. Group like terms: Now, we group the terms with the same variable and exponent together: $(6x^2 - 6x^2) + (-2x + 7x) + (6 + 2)$.
5. Combine like terms: Perform the addition or subtraction for each group of like terms:
- For the $x^2$ terms: $6x^2 - 6x^2 = 0x^2 = 0$
- For the $x$ terms: $-2x + 7x = 5x$
- For the constant terms: $6 + 2 = 8$
6. Write the final expression: Combine the results from the previous step to get the simplified expression: $0 + 5x + 8 = 5x + 8$.