https://file.aiquickdraw.com/mathbot/file/1725822138458o8391bnf.jpg

To solve the problem in the image, we need to subtract the second polynomial from the first and then simplify the expression.

### Given:
\[
(3x^3 - 6x^2 + 4x - 10) - (7x^3 - 6x^2 - 7x + 6)
\]

### Step 1: Distribute the negative sign through the second polynomial:
\[
3x^3 - 6x^2 + 4x - 10 - 7x^3 + 6x^2 + 7x - 6
\]

### Step 2: Combine like terms:
- For \(x^3\) terms: \(3x^3 - 7x^3 = -4x^3\)
- For \(x^2\) terms: \(-6x^2 + 6x^2 = 0\) (the \(x^2\) terms cancel out)
- For \(x\) terms: \(4x + 7x = 11x\)
- For constant terms: \(-10 - 6 = -16\)

### Step 3: Write the final polynomial in standard form:
\[
-4x^3 + 11x - 16
\]

The polynomial in standard form after performing the indicated operation is:

\[
\boxed{-4x^3 + 11x - 16}
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How do you add or subtract polynomials with different degrees?
2. What happens when you combine like terms in polynomial operations?
3. Can you explain how the distributive property applies when subtracting polynomials?
4. How would the answer change if the signs of the terms in the second polynomial were reversed?
5. What is the importance of writing a polynomial in standard form?

**Tip:** When subtracting polynomials, always distribute the negative sign to each term in the polynomial being subtracted before combining like terms.

Perform the operation: (3x^3 - 6x^2 + 4x - 10) - (7x^3 - 6x^2 - 7x + 6)

Learn how to subtract two polynomials (3x^3 - 6x^2 + 4x - 10) and (7x^3 - 6x^2 - 7x + 6) step by step, distributing the negative sign and combining like terms. This problem demonstrates core concepts in algebra, particularly polynomial operations, suitable for students in Grades 9-12.

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