(5x^3-x+2x^2)+(7-4x)-(6x^2+5x^3-3)

2 min read Jun 16, 2024
(5x^3-x+2x^2)+(7-4x)-(6x^2+5x^3-3)

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression: (5x^3 - x + 2x^2) + (7 - 4x) - (6x^2 + 5x^3 - 3)

Understanding the Steps

To simplify this expression, we will follow these steps:

  1. Remove parentheses: We will distribute any negative signs in front of parentheses.
  2. Combine like terms: We will group together terms with the same variable and exponent.
  3. Simplify: We will perform the necessary arithmetic operations.

Simplifying the Expression

Let's break down the simplification process step by step:

  1. Removing parentheses:

    • The first set of parentheses doesn't have a negative sign in front, so we can simply remove them.
    • The second set of parentheses also doesn't have a negative sign in front.
    • The third set of parentheses has a negative sign in front. We distribute this negative sign to each term inside the parentheses:
      • -(6x^2 + 5x^3 - 3) = -6x^2 - 5x^3 + 3
  2. Combining like terms:

    • x^3 terms: 5x^3 - 5x^3 = 0x^3 (these terms cancel out)
    • x^2 terms: 2x^2 - 6x^2 = -4x^2
    • x terms: -x - 4x = -5x
    • Constant terms: 7 + 3 = 10
  3. Simplifying:

    Putting all the simplified terms together, we get:

    0x^3 - 4x^2 - 5x + 10

Final Answer

Therefore, the simplified form of the given polynomial expression is -4x^2 - 5x + 10.

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