Let's perform the indicated operation by subtracting the two polynomials:

The given expression is: $(7x^3 - 7x^2 + 3x - 7) - (2x^3 - 3x^2 - 5x + 5)$

To subtract the second polynomial, distribute the negative sign:

$= (7x^3 - 7x^2 + 3x - 7) - 2x^3 + 3x^2 + 5x - 5$

Now, combine like terms:

• $7x^3 - 2x^3 = 5x^3$
• $-7x^2 + 3x^2 = -4x^2$
• $3x + 5x = 8x$
• $-7 - 5 = -12$

So, the polynomial in standard form is: $5x^3 - 4x^2 + 8x - 12$

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What is the result of subtracting $(6x^3 + 4x^2 - 5)$ from $(8x^3 - 2x^2 + 7)$?
2. How do you add the polynomials $(3x^3 - 2x^2 + x - 4)$ and $(5x^3 + x^2 - 3x + 6)$?
3. What is the degree of the polynomial $9x^4 - 6x^3 + 2x^2 - 7x + 10$?
4. How do you factor the polynomial $4x^2 - 16$?
5. How can you determine the leading coefficient of a polynomial?

Tip: When subtracting polynomials, always distribute the negative sign to each term in the second polynomial before combining like terms!