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

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Jun 07, 2024

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Simplifying Algebraic Expressions: A Step-by-Step Guide

The Expression: (x^3+6x^2+5y^3)-(2x^3-5x+7y^3)

In this article, we will simplify the algebraic expression (x^3+6x^2+5y^3)-(2x^3-5x+7y^3). To simplify this expression, we will follow the order of operations (PEMDAS) and combine like terms.

Step 1: Distribute the Negative Sign

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

x^3 + 6x^2 + 5y^3 - 2x^3 + 5x - 7y^3

Step 2: Combine Like Terms

Now, let's combine like terms:

• The x^3 terms: x^3 - 2x^3 = -x^3
• The x^2 terms: 6x^2 (no like terms to combine)
• The x terms: 5x (no like terms to combine)
• The y^3 terms: 5y^3 - 7y^3 = -2y^3

Step 3: Write the Simplified Expression

Finally, we can write the simplified expression:

-x^3 + 6x^2 + 5x - 2y^3

And that's it! We have successfully simplified the expression (x^3+6x^2+5y^3)-(2x^3-5x+7y^3).