x^4 + 2x^3 - 8x - 18x + 2

To simplify the expression x 4 + 2 x 3 − 8 x − 18 x + 2 , we combine the like terms − 8 x and − 18 x to get − 26 x . The final simplified expression is x 4 + 2 x 3 − 26 x + 2 .
;

Answered by Anonymous | 2025-07-04

Combine like terms: − 8 x − 18 x = − 26 x .
Substitute the combined term back into the original expression.
The simplified expression is x 4 + 2 x 3 − 26 x + 2 .
The final simplified expression is x 4 + 2 x 3 − 26 x + 2 ​ .

Explanation

Understanding the Problem We are given the expression x 4 + 2 x 3 − 8 x − 18 x + 2 and asked to simplify it. This involves combining like terms.

Combining Like Terms The like terms in the expression are the terms involving x , which are − 8 x and − 18 x . We combine these terms by adding their coefficients: − 8 + ( − 18 ) = − 26 . Therefore, − 8 x − 18 x = − 26 x .

Simplified Expression Substituting this back into the original expression, we get x 4 + 2 x 3 − 26 x + 2 . There are no other like terms to combine, so this is the simplified expression.

Final Answer Therefore, the simplified expression is x 4 + 2 x 3 − 26 x + 2 .


Examples
Simplifying polynomial expressions is a fundamental skill in algebra and is used in many real-world applications. For example, engineers use polynomials to model the behavior of structures and circuits. Simplifying these expressions allows them to analyze and design systems more efficiently. In computer graphics, polynomials are used to represent curves and surfaces. Simplifying these polynomial expressions can optimize the rendering process and improve the performance of graphical applications. Understanding how to simplify polynomial expressions is essential for success in many STEM fields.

Answered by GinnyAnswer | 2025-07-04