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(-n^2+2n)-(2n^3-n^2+n+12)

2 min read Jun 16, 2024
(-n^2+2n)-(2n^3-n^2+n+12)

Simplifying the Expression: (-n^2+2n)-(2n^3-n^2+n+12)

This article will guide you through simplifying the algebraic expression: (-n^2+2n)-(2n^3-n^2+n+12).

Understanding the Problem

The expression involves subtracting one polynomial from another. To simplify it, we'll need to:

  1. Distribute the negative sign: The minus sign before the second set of parentheses means we need to multiply each term inside the parentheses by -1.
  2. Combine like terms: After distributing the negative sign, we'll have terms with the same variable and exponent. We can then combine these terms by adding or subtracting their coefficients.

Step-by-Step Simplification

  1. Distribute the negative sign:

    (-n^2+2n) + (-1)(2n^3-n^2+n+12)

    = -n^2 + 2n - 2n^3 + n^2 - n - 12

  2. Combine like terms:

    -2n^3 + (-n^2 + n^2) + (2n - n) - 12

    = -2n^3 + n - 12

Final Result

The simplified expression is -2n^3 + n - 12.

Key Points to Remember

  • Order of Operations: Always remember to follow the order of operations (PEMDAS/BODMAS).
  • Distribute Carefully: When distributing a negative sign, make sure to multiply each term within the parentheses by -1.
  • Combine Like Terms: Combine terms with the same variable and exponent to simplify the expression.

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