(-3x^4+6x^3-11x^2+5)-(5x^4+2x^3-x)

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Jun 03, 2024

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Simplifying Algebraic Expressions: A Step-by-Step Guide

In this article, we will explore how to simplify the algebraic expression -3x^4 + 6x^3 - 11x^2 + 5 - (5x^4 + 2x^3 - x). We will break down the steps to combine like terms and simplify the expression.

Step 1: Distribute the Negative Sign

First, we need to distribute the negative sign to the terms inside the parentheses:

-3x^4 + 6x^3 - 11x^2 + 5 - 5x^4 - 2x^3 + x

Step 2: Combine Like Terms

Now, we will combine like terms:

x^4 terms: -3x^4 - 5x^4 = -8x^4

x^3 terms: 6x^3 - 2x^3 = 4x^3

x^2 terms: -11x^2 (no other x^2 terms to combine with)

x terms: x (no other x terms to combine with)

Constant terms: 5 (no other constant terms to combine with)

Step 3: Write the Simplified Expression

Now, we can write the simplified expression:

-8x^4 + 4x^3 - 11x^2 + x + 5

And that's it! We have successfully simplified the algebraic expression -3x^4 + 6x^3 - 11x^2 + 5 - (5x^4 + 2x^3 - x).