(-5n^2+7n^3+5n)-(2n^3-8n^4+5n^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

In this article, we will simplify the expression: (-5n^2 + 7n^3 + 5n) - (2n^3 - 8n^4 + 5n^2).

To simplify this expression, we need to understand the following:

• Combining like terms: We can only add or subtract terms that have the same variable and exponent.
• Distributing the negative sign: The minus sign in front of the parentheses means we multiply each term inside the parentheses by -1.

Let's break down the simplification step by step:

1. Distribute the negative sign: (-5n^2 + 7n^3 + 5n) + (-1 * 2n^3) + (-1 * -8n^4) + (-1 * 5n^2)

2. Simplify: -5n^2 + 7n^3 + 5n - 2n^3 + 8n^4 - 5n^2

3. Combine like terms: 8n^4 + (7n^3 - 2n^3) + (-5n^2 - 5n^2) + 5n

4. Final simplified expression: 8n^4 + 5n^3 - 10n^2 + 5n

Therefore, the simplified form of the expression (-5n^2 + 7n^3 + 5n) - (2n^3 - 8n^4 + 5n^2) is 8n^4 + 5n^3 - 10n^2 + 5n.