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

Question

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Solution

1. ### Break Down the Problem

We need to simplify the expression (6x3+3x2+8)+(2x29x+10)(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 (6x3+3x2+8)+(2x29x+10)=6x3+(3x2+2x2)+(9x)+(8+10) (6x^3 + 3x^2 + 8) + (2x^2 - 9x + 10) = 6x^3 + (3x^2 + 2x^2) + (-9x) + (8 + 10) Combine the like terms:

  • 6x36x^3
  • 3x2+2x2=5x23x^2 + 2x^2 = 5x^2
  • 9x-9x
  • 8+10=188 + 10 = 18

Thus, the simplified expression is: 6x3+5x29x+18 6x^3 + 5x^2 - 9x + 18

Step 2: Simplify the large expression Now, we examine the expression provided: 8x56x3+185x4+6x39x+186x3+5x29x+186x3+x2+9x2 8x^5 - 6x^3 + 185x^4 + 6x^3 - 9x + 186x^3 + 5x^2 - 9x + 186x^3 + x^2 + 9x - 2 Combine like terms:

  • 8x58x^5 (only one term)
  • 185x4185x^4 (only one term)
  • 6x3+6x3+186x3+186x3=372x3-6x^3 + 6x^3 + 186x^3 + 186x^3 = 372x^3
  • 9x9x+9x=9x-9x - 9x + 9x = -9x
  • 5x2+x2=6x25x^2 + x^2 = 6x^2
  • Constant term: 2-2

Thus, the simplified large expression becomes: 8x5+185x4+372x3+6x29x2 8x^5 + 185x^4 + 372x^3 + 6x^2 - 9x - 2

4. ### Verify and Summarize

To summarize:

  • The simplified first expression is 6x3+5x29x+186x^3 + 5x^2 - 9x + 18.
  • The simplified large expression is 8x5+185x4+372x3+6x29x28x^5 + 185x^4 + 372x^3 + 6x^2 - 9x - 2.

Final Answer

The two expressions are not equivalent. The first expression simplifies to 6x3+5x29x+186x^3 + 5x^2 - 9x + 18, while the second simplifies to 8x5+185x4+372x3+6x29x28x^5 + 185x^4 + 372x^3 + 6x^2 - 9x - 2.

This problem has been solved

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