https://file.aiquickdraw.com/mathbot/file/1728941054063cwpxvc9i.jpg

Let's solve the problem step by step.

We have:
\[
(3x^3 - 2x^2 + 4x - 8) - (5x^3 + 12x^2 - 3x - 4)
\]

To find the difference, we need to distribute the negative sign to each term in the second polynomial and then combine like terms:

1. Distribute the negative:
   \[
   3x^3 - 2x^2 + 4x - 8 - 5x^3 - 12x^2 + 3x + 4
   \]

2. Combine like terms:
   - For \(x^3\): \(3x^3 - 5x^3 = -2x^3\)
   - For \(x^2\): \(-2x^2 - 12x^2 = -14x^2\)
   - For \(x\): \(4x + 3x = 7x\)
   - For the constant: \(-8 + 4 = -4\)

Thus, the correct result is:
\[
-2x^3 - 14x^2 + 7x - 4
\]

The provided answer, \(-2x^3 - 14x^2 - 7x - 4\), had an incorrect sign for the linear term \(7x\). 

Would you like further details or have any questions?

### Related Questions:
1. How do you add polynomials?
2. What is the process for combining like terms?
3. How does the distributive property work in polynomial subtraction?
4. How can polynomial subtraction be visualized on a graph?
5. What are common mistakes when subtracting polynomials?

**Tip:** Always double-check the signs when distributing a negative across a polynomial.

(3x^3 - 2x^2 + 4x - 8) - (5x^3 + 12x^2 - 3x - 4)

Learn how to subtract two polynomials step-by-step: (3x^3 - 2x^2 + 4x - 8) - (5x^3 + 12x^2 - 3x - 4). This solution explores key algebraic concepts such as combining like terms and using the distributive property. Suitable for students in Grades 9-11.

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