Simplify the following expression: [tex]x^3-3 x+2 x+2[/tex]

The expression x 3 − 3 x + 2 x + 2 simplifies to x 3 − x + 2 by combining the like terms. We identify − 3 x and + 2 x as like terms, combine them to get − x , and rewrite the expression accordingly. The final result is x 3 − x + 2 ​ .
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Answered by Anonymous | 2025-07-04

Identify like terms: − 3 x and + 2 x .
Combine like terms: − 3 x + 2 x = − x .
Substitute the combined term back into the original expression: x 3 − 3 x + 2 x + 2 = x 3 − x + 2 .
The simplified expression is x 3 − x + 2 ​ .

Explanation

Understanding the Problem We are given the expression x 3 − 3 x + 2 x + 2 and our goal is to simplify it by combining like terms.

Identifying Like Terms First, we identify the like terms in the expression. The terms − 3 x and + 2 x are like terms because they both contain the variable x raised to the power of 1.

Combining Like Terms Next, we combine the like terms: − 3 x + 2 x = − 1 x = − x .

Writing the Simplified Expression Now, we substitute the combined term back into the original expression: x 3 − 3 x + 2 x + 2 = x 3 − x + 2 . This is the simplified form of the given expression.

Final Answer Therefore, the simplified expression is x 3 − x + 2 .


Examples
Simplifying algebraic expressions is a fundamental skill in mathematics. For instance, if you are calculating the volume of a 3D shape and arrive at an expression like x 3 − 3 x + 2 x + 2 , simplifying it to x 3 − x + 2 makes it easier to understand how the volume changes with respect to x . This skill is also crucial in physics, engineering, and computer science, where complex equations often need to be simplified for analysis and problem-solving.

Answered by GinnyAnswer | 2025-07-04