We appreciate your visit to Simplify the expression tex left 2x 3x 4 3 right left 8 14x 4 4x right tex Choose the correct simplified expression A tex 26x. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Distribute the negative sign: $-2x + 3x^4 + 3 + 8 + 14x^4 - 4x$.
- Combine the $x^4$ terms: $3x^4 + 14x^4 = 17x^4$.
- Combine the $x$ terms: $-2x - 4x = -6x$.
- Combine the constants: $3 + 8 = 11$. The simplified expression is $\boxed{17x^4 - 6x + 11}$.
### Explanation
1. Distribute the Negative Sign
Let's simplify the given expression step by step: $\left(-2 x+3 x^4+3\right)-\left(-8-14 x^4+4 x\right)$. First, distribute the negative sign in the second parenthesis: $-2x + 3x^4 + 3 + 8 + 14x^4 - 4x$.
2. Combine Like Terms
Now, combine like terms. We have terms with $x^4$, $x$, and constants. Combining the $x^4$ terms: $3x^4 + 14x^4 = 17x^4$. Combining the $x$ terms: $-2x - 4x = -6x$. Combining the constants: $3 + 8 = 11$.
3. Simplified Expression
So the simplified expression is $17x^4 - 6x + 11$. Now, let's compare this with the given options to find the correct one.
4. Final Answer
The simplified expression matches the last option: $17 x^4-6 x+11$. Therefore, the correct answer is $17 x^4-6 x+11$.
### Examples
Polynomials are used to model curves and shapes in various fields such as engineering, computer graphics, and physics. For example, engineers use polynomials to design bridges and buildings, while computer graphics designers use them to create realistic images. Understanding how to simplify polynomial expressions is essential for solving real-world problems in these fields.
- Combine the $x^4$ terms: $3x^4 + 14x^4 = 17x^4$.
- Combine the $x$ terms: $-2x - 4x = -6x$.
- Combine the constants: $3 + 8 = 11$. The simplified expression is $\boxed{17x^4 - 6x + 11}$.
### Explanation
1. Distribute the Negative Sign
Let's simplify the given expression step by step: $\left(-2 x+3 x^4+3\right)-\left(-8-14 x^4+4 x\right)$. First, distribute the negative sign in the second parenthesis: $-2x + 3x^4 + 3 + 8 + 14x^4 - 4x$.
2. Combine Like Terms
Now, combine like terms. We have terms with $x^4$, $x$, and constants. Combining the $x^4$ terms: $3x^4 + 14x^4 = 17x^4$. Combining the $x$ terms: $-2x - 4x = -6x$. Combining the constants: $3 + 8 = 11$.
3. Simplified Expression
So the simplified expression is $17x^4 - 6x + 11$. Now, let's compare this with the given options to find the correct one.
4. Final Answer
The simplified expression matches the last option: $17 x^4-6 x+11$. Therefore, the correct answer is $17 x^4-6 x+11$.
### Examples
Polynomials are used to model curves and shapes in various fields such as engineering, computer graphics, and physics. For example, engineers use polynomials to design bridges and buildings, while computer graphics designers use them to create realistic images. Understanding how to simplify polynomial expressions is essential for solving real-world problems in these fields.
Thanks for taking the time to read Simplify the expression tex left 2x 3x 4 3 right left 8 14x 4 4x right tex Choose the correct simplified expression A tex 26x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
