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(-4x+2x^3-5)+(6x^2-3x+6x^3)+(13-2x^2+9x-8x^2)

2 min read Jun 16, 2024
(-4x+2x^3-5)+(6x^2-3x+6x^3)+(13-2x^2+9x-8x^2)

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(-4x+2x^3-5)+(6x^2-3x+6x^3)+(13-2x^2+9x-8x^2)

Step 1: Identify Like Terms

First, we need to identify the terms that have the same variable and exponent.

  • x^3 terms: 2x^3 + 6x^3
  • x^2 terms: 6x^2 - 2x^2 - 8x^2
  • x terms: -4x - 3x + 9x
  • Constant terms: -5 + 13

Step 2: Combine Like Terms

Now, we combine the coefficients of the like terms.

  • x^3 terms: 2x^3 + 6x^3 = 8x^3
  • x^2 terms: 6x^2 - 2x^2 - 8x^2 = -4x^2
  • x terms: -4x - 3x + 9x = 2x
  • Constant terms: -5 + 13 = 8

Step 3: Write the Simplified Expression

Finally, we arrange the terms in descending order of their exponents.

Simplified Expression: 8x^3 - 4x^2 + 2x + 8

Therefore, the simplified form of the given polynomial expression is 8x^3 - 4x^2 + 2x + 8.

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