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Answer :
- Combine like terms: $-2x^4 + 2x^4 = 0$ and $16 + 9 = 25$.
- Simplify the expression: $25 - 3x^5$.
- Write in standard form (decreasing order of exponents): $-3x^5 + 25$.
- The simplified expression is $\boxed{{-3x^5 + 25}}$.
### Explanation
1. Understanding the Problem
We are given the expression $-2 x^4+16+2 x^4+9-3 x^5$ and asked to simplify it. This involves combining like terms and writing the result in standard form (decreasing order of exponents).
2. Identifying Like Terms
First, let's identify the like terms. We have $-2x^4$ and $+2x^4$, which are like terms. Also, $16$ and $9$ are like terms (constants).
3. Combining Like Terms
Now, let's combine the like terms:
$-2x^4 + 2x^4 = 0$
$16 + 9 = 25$
4. Simplifying the Expression
After combining like terms, the expression becomes:
$0 + 25 - 3x^5$
Which simplifies to:
$25 - 3x^5$
5. Final Answer
Finally, we write the simplified expression in standard form (decreasing order of exponents):
$-3x^5 + 25$
So, the simplified expression is $\boxed{{-3x^5 + 25}}$.
### Examples
Polynomials are used to model various real-world phenomena, such as the trajectory of a ball, the shape of a bridge, or the growth of a population. Simplifying polynomial expressions allows us to analyze these models more easily and make predictions about the systems they represent. For instance, if we have a polynomial representing the profit of a company, simplifying it can help us determine the factors that contribute most to the profit and make informed business decisions.
- Simplify the expression: $25 - 3x^5$.
- Write in standard form (decreasing order of exponents): $-3x^5 + 25$.
- The simplified expression is $\boxed{{-3x^5 + 25}}$.
### Explanation
1. Understanding the Problem
We are given the expression $-2 x^4+16+2 x^4+9-3 x^5$ and asked to simplify it. This involves combining like terms and writing the result in standard form (decreasing order of exponents).
2. Identifying Like Terms
First, let's identify the like terms. We have $-2x^4$ and $+2x^4$, which are like terms. Also, $16$ and $9$ are like terms (constants).
3. Combining Like Terms
Now, let's combine the like terms:
$-2x^4 + 2x^4 = 0$
$16 + 9 = 25$
4. Simplifying the Expression
After combining like terms, the expression becomes:
$0 + 25 - 3x^5$
Which simplifies to:
$25 - 3x^5$
5. Final Answer
Finally, we write the simplified expression in standard form (decreasing order of exponents):
$-3x^5 + 25$
So, the simplified expression is $\boxed{{-3x^5 + 25}}$.
### Examples
Polynomials are used to model various real-world phenomena, such as the trajectory of a ball, the shape of a bridge, or the growth of a population. Simplifying polynomial expressions allows us to analyze these models more easily and make predictions about the systems they represent. For instance, if we have a polynomial representing the profit of a company, simplifying it can help us determine the factors that contribute most to the profit and make informed business decisions.
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