Simplifying the Expression: (2x^3 - 5x^2-5x) + (5x^3 - x^2 +4x+4)

As a high school mathematics teacher, one of the fundamental skills I aim to develop in my students is the ability to simplify algebraic expressions. This not only helps them understand the underlying mathematical concepts but also prepares them for more advanced problem-solving in higher-level mathematics.

In this article, we will walk through the step-by-step process of simplifying the expression: (2x^3 - 5x^2-5x) + (5x^3 - x^2 +4x+4).

Step 1: Identify the Like Terms

The first step in simplifying this expression is to identify the like terms. Like terms are terms that have the same variable raised to the same power. In our expression, we have the following like terms:

• 2x^3 and 5x^3
• -5x^2 and -x^2
• -5x and 4x

Step 2: Combine the Like Terms

Now that we have identified the like terms, we can combine them by adding their coefficients together.

• 2x^3 + 5x^3 = 7x^3
• -5x^2 - x^2 = -6x^2
• -5x + 4x = -x
• 4 (no like term to combine)

Step 3: Write the Simplified Expression

Putting it all together, the simplified expression is: 7x^3 - 6x^2 - x + 4

This is the final answer, and the expression has been simplified to its simplest form.

By breaking down the process step-by-step, students can better understand the underlying concepts and develop the skills necessary to simplify more complex algebraic expressions in the future.