https://r2.erweima.ai/mathbot/image/1725427530643errmq73u.jpg

The expression given in the image is:

\[ 85x^2 + \left(19x^2 - 3x^3\right) - \left[6x^2 + \left(5x^2 - 3x^3\right) - \left(2x^2 + 1x^3\right) + \left(5x^2 - 3x^3\right)\right] \]

To simplify this expression, let's proceed step by step:

1. **Expand and combine like terms** inside the brackets.
   
   Start with the innermost brackets:

   \[
   5x^2 - 3x^3 - \left(2x^2 + 1x^3\right) + \left(5x^2 - 3x^3\right)
   \]

   Distribute the minus sign inside the first parenthesis:

   \[
   5x^2 - 3x^3 - 2x^2 - 1x^3 + 5x^2 - 3x^3
   \]

   Combine like terms:

   \[
   (5x^2 - 2x^2 + 5x^2) + (-3x^3 - 1x^3 - 3x^3) = 8x^2 - 7x^3
   \]

   Now, go back to the original expression, substituting the simplified expression:

   \[
   85x^2 + (19x^2 - 3x^3) - (6x^2 + 8x^2 - 7x^3)
   \]

2. **Simplify further** by distributing and combining like terms:

   \[
   85x^2 + 19x^2 - 3x^3 - 6x^2 - 8x^2 + 7x^3
   \]

   Combine the \(x^2\) terms:

   \[
   (85x^2 + 19x^2 - 6x^2 - 8x^2) + (-3x^3 + 7x^3) = 90x^2 + 4x^3
   \]

So, the simplified expression is:

\[
90x^2 + 4x^3
\]

Would you like further details or have any questions? 

Here are some related questions you might find useful:
1. What are like terms, and why do we combine them?
2. How do you distribute a minus sign across parentheses?
3. What are the steps to factorize the final expression \(90x^2 + 4x^3\)?
4. Can this expression be simplified further by factoring?
5. How would you apply these steps to an expression with more variables?

**Tip:** Always ensure to carefully distribute and combine like terms when simplifying expressions to avoid mistakes.

Reducir los términos de la expresión algebraica dada: 85x^2 + (19x^2 - 3x^3) - [6x^2 + (5x^2 - 3x^3) - (2x^2 + 1x^3) + (5x^2 - 3x^3)]

Learn how to simplify polynomial expressions by combining like terms and using the distributive property. This guide walks you through reducing the expression 85x^2 + (19x^2 - 3x^3) - [6x^2 + (5x^2 - 3x^3) - (2x^2 + 1x^3) + (5x^2 - 3x^3)] with detailed steps. Ideal for students in Grades 8-10.

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