Which expression is equivalent to (6x3+3x2+8)+(2x2−9x+10)?8x5−6x3+185x4+6x3−9x+186x3+5x2−9x+186x3+x2+9x−2

1. ### Break Down the Problem

We need to simplify the expression $(6x^3 + 3x^2 + 8) + (2x^2 - 9x + 10)$ and compare it with the large expression provided.

2. ### Relevant Concepts

To simplify, we will:

• Combine like terms in the initial expression.
• Expand and then combine the like terms in the second expression to see if they match.

3. ### Analysis and Detail

Step 1: Simplify the first expression $(6x^3 + 3x^2 + 8) + (2x^2 - 9x + 10) = 6x^3 + (3x^2 + 2x^2) + (-9x) + (8 + 10)$ Combine the like terms:

• $6x^3$
• $3x^2 + 2x^2 = 5x^2$
• $-9x$
• $8 + 10 = 18$

Thus, the simplified expression is: $6x^3 + 5x^2 - 9x + 18$

Step 2: Simplify the large expression Now, we examine the expression provided: $8x^5 - 6x^3 + 185x^4 + 6x^3 - 9x + 186x^3 + 5x^2 - 9x + 186x^3 + x^2 + 9x - 2$ Combine like terms:

• $8x^5$ (only one term)
• $185x^4$ (only one term)
• $-6x^3 + 6x^3 + 186x^3 + 186x^3 = 372x^3$
• $-9x - 9x + 9x = -9x$
• $5x^2 + x^2 = 6x^2$
• Constant term: $-2$

Thus, the simplified large expression becomes: $8x^5 + 185x^4 + 372x^3 + 6x^2 - 9x - 2$

4. ### Verify and Summarize

To summarize:

• The simplified first expression is $6x^3 + 5x^2 - 9x + 18$.
• The simplified large expression is $8x^5 + 185x^4 + 372x^3 + 6x^2 - 9x - 2$.

Final Answer

The two expressions are not equivalent. The first expression simplifies to $6x^3 + 5x^2 - 9x + 18$, while the second simplifies to $8x^5 + 185x^4 + 372x^3 + 6x^2 - 9x - 2$.