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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!

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

Learn how to subtract two polynomials with the example (7x^3 - 7x^2 + 3x - 7) - (2x^3 - 3x^2 - 5x + 5). This step-by-step guide covers polynomial subtraction and the combining of like terms. Suitable for students in Grades 8-10.

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