Simplify The Expression:$x^x + 0x^3 - 25x^2 + 0x + 144$

Introduction

In this article, we will simplify the given expression: $x^x + 0x^3 - 25x^2 + 0x + 144$. This expression involves various mathematical operations, including exponentiation, multiplication, and addition. Our goal is to simplify this expression by combining like terms and applying mathematical rules.

Understanding the Expression

The given expression is a polynomial of degree $x^x$, which is a non-standard polynomial. However, we can simplify it by considering the terms with the same power of $x$. The expression can be written as:

$$x^x + 0x^3 - 25x^2 + 0x + 144$$

Simplifying the Expression

To simplify the expression, we need to combine like terms. The like terms are the terms with the same power of $x$. In this expression, we have two like terms: $0x^3$ and $0x$. Since both terms have the same power of $x$, we can combine them.

$$x^x + 0x^3 - 25x^2 + 0x + 144 = x^x - 25x^2 + 144$$

Applying Mathematical Rules

Now, we can apply mathematical rules to simplify the expression further. We can start by simplifying the term $x^x$. Since $x^x$ is a non-standard polynomial, we cannot simplify it using standard algebraic rules. However, we can rewrite it as:

$$x^x = e^{x \ln x}$$

where $e$ is the base of the natural logarithm and $\ln x$ is the natural logarithm of $x$.

Substituting the Expression

Now, we can substitute the expression $x^x = e^{x \ln x}$ into the simplified expression:

$$x^x - 25x^2 + 144 = e^{x \ln x} - 25x^2 + 144$$

Simplifying the Expression Further

We can simplify the expression further by combining the like terms. The like terms are the terms with the same power of $x$. In this expression, we have two like terms: $-25x^2$ and $144$. Since both terms have the same power of $x$, we can combine them.

$$e^{x \ln x} - 25x^2 + 144 = e^{x \ln x} - 25x^2 + 144$$

However, we can rewrite the expression as:

$$e^{x \ln x} - 25x^2 + 144 = e^{x \ln x} - 25x^2 + 144$$

Conclusion

In this article, we simplified the given expression: $x^x + 0x^3 - 25x^2 + 0x + 144$. We combined like terms and applied mathematical rules to simplify the expression. The final simplified expression is:

$$e^{x \ln x} - 25x^2 + 144$$

Final Answer

The final answer is $\boxed{e^{x \ln x} - 25x^2 + 144}$.

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Mathematics for Computer Science" by Eric Lehman

Glossary

• Exponentiation: The operation of raising a number to a power.
• Multiplication: The operation of combining two or more numbers to produce a product.
• Addition: The operation of combining two or more numbers to produce a sum.
• Polynomial: An expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.
• Like terms: Terms with the same power of a variable.
• Natural logarithm: The logarithm of a number to the base $e$.
• Base of the natural logarithm: The number $e$.
• Simplify: To reduce an expression to its simplest form.
  Simplify the Expression: A Q&A Guide =====================================

Introduction

In our previous article, we simplified the given expression: $x^x + 0x^3 - 25x^2 + 0x + 144$. We combined like terms and applied mathematical rules to simplify the expression. In this article, we will answer some frequently asked questions related to the simplification of the expression.

Q&A

Q: What is the final simplified expression?

A: The final simplified expression is $e^{x \ln x} - 25x^2 + 144$.

Q: How did you simplify the expression?

A: We combined like terms and applied mathematical rules to simplify the expression. We started by combining the like terms $0x^3$ and $0x$, and then we applied the rule of exponentiation to simplify the term $x^x$.

Q: What is the significance of the term $e^{x \ln x}$?

A: The term $e^{x \ln x}$ is a non-standard polynomial, and it cannot be simplified using standard algebraic rules. However, it can be rewritten as $e^{x \ln x} = x^x$.

Q: Can you explain the concept of like terms?

A: Like terms are terms with the same power of a variable. In the expression $x^x + 0x^3 - 25x^2 + 0x + 144$, the like terms are $0x^3$ and $0x$, and the like terms are also $-25x^2$ and $144$.

Q: What is the difference between the natural logarithm and the base of the natural logarithm?

A: The natural logarithm is the logarithm of a number to the base $e$, and the base of the natural logarithm is the number $e$ itself.

Q: Can you provide more examples of simplifying expressions?

A: Yes, here are a few examples:

• Simplify the expression $x^2 + 3x - 4$.
• Simplify the expression $2x^3 - 5x^2 + 3x - 1$.
• Simplify the expression $x^4 + 2x^3 - 3x^2 + x - 1$.

Q: How do you determine if an expression can be simplified?

A: An expression can be simplified if it contains like terms or if it can be rewritten using mathematical rules.

Q: What are some common mathematical rules used to simplify expressions?

A: Some common mathematical rules used to simplify expressions include:

• The rule of exponentiation: $a^m \cdot a^n = a^{m+n}$
• The rule of multiplication: $a \cdot b = b \cdot a$
• The rule of addition: $a + b = b + a$
• The rule of subtraction: $a - b = b - a$

Conclusion

In this article, we answered some frequently asked questions related to the simplification of the expression $x^x + 0x^3 - 25x^2 + 0x + 144$. We explained the concept of like terms, the significance of the term $e^{x \ln x}$, and provided examples of simplifying expressions. We also discussed some common mathematical rules used to simplify expressions.

Final Answer

The final answer is $\boxed{e^{x \ln x} - 25x^2 + 144}$.

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Mathematics for Computer Science" by Eric Lehman

Glossary

• Exponentiation: The operation of raising a number to a power.
• Multiplication: The operation of combining two or more numbers to produce a product.
• Addition: The operation of combining two or more numbers to produce a sum.
• Polynomial: An expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.
• Like terms: Terms with the same power of a variable.
• Natural logarithm: The logarithm of a number to the base $e$.
• Base of the natural logarithm: The number $e$.
• Simplify: To reduce an expression to its simplest form.