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(2x^4-3x^3+2x-1)-(x^4-x^2+2x+3)

2 min read Jun 16, 2024
(2x^4-3x^3+2x-1)-(x^4-x^2+2x+3)

Simplifying Polynomial Expressions

This article will explore how to simplify the expression (2x^4 - 3x^3 + 2x - 1) - (x^4 - x^2 + 2x + 3).

Understanding the Problem

We are tasked with subtracting one polynomial expression from another. To do this, we need to follow the steps below:

  1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we need to multiply each term inside by -1.

  2. Combine like terms: After distributing the negative sign, we will have terms with the same variable and exponent. We will combine these terms.

Solving the Problem

Let's follow the steps outlined above:

  1. Distribute the negative sign:

    (2x^4 - 3x^3 + 2x - 1) + (-1)(x^4 - x^2 + 2x + 3)

    This gives us:

    2x^4 - 3x^3 + 2x - 1 - x^4 + x^2 - 2x - 3

  2. Combine like terms:

    (2x^4 - x^4) + (-3x^3) + (x^2) + (2x - 2x) + (-1 - 3)

    This simplifies to:

    x^4 - 3x^3 + x^2 - 4

Conclusion

Therefore, the simplified form of the expression (2x^4 - 3x^3 + 2x - 1) - (x^4 - x^2 + 2x + 3) is x^4 - 3x^3 + x^2 - 4.

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