Simplify The Expression: \left(4x + X^2 - 9\right) + \left(11 - 3x + 5x^2\right ]

===========================================================

Introduction

---

In algebra, simplifying expressions is a crucial step in solving equations and inequalities. One of the fundamental concepts in simplifying expressions is combining like terms. In this article, we will focus on simplifying the given expression: $\left(4x + x^2 - 9\right) + \left(11 - 3x + 5x^2\right)$. We will break down the process of combining like terms and provide a step-by-step guide on how to simplify the expression.

Understanding Like Terms

---

Like terms are terms that have the same variable raised to the same power. In other words, like terms are terms that have the same exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1. Similarly, $x^2$ and $3x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Combining Like Terms

---

Combining like terms involves adding or subtracting the coefficients of like terms. The coefficient of a term is the number that is multiplied by the variable. For example, in the term $2x$, the coefficient is 2. In the term $5x$, the coefficient is 5.

To combine like terms, we need to follow these steps:

1. Identify the like terms in the expression.
2. Add or subtract the coefficients of the like terms.
3. Simplify the resulting expression.

Simplifying the Expression

---

Now that we have understood the concept of like terms and how to combine them, let's simplify the given expression: $\left(4x + x^2 - 9\right) + \left(11 - 3x + 5x^2\right)$.

Step 1: Identify the Like Terms

---

The first step in simplifying the expression is to identify the like terms. In this expression, we have the following like terms:

• $4x$ and $-3x$
• $x^2$ and $5x^2$
• $-9$ and $11$

Step 2: Combine the Like Terms

---

Now that we have identified the like terms, let's combine them.

• $4x$ and $-3x$ can be combined by adding their coefficients: $4x - 3x = x$
• $x^2$ and $5x^2$ can be combined by adding their coefficients: $x^2 + 5x^2 = 6x^2$
• $-9$ and $11$ can be combined by adding their coefficients: $-9 + 11 = 2$

Step 3: Simplify the Expression

---

Now that we have combined the like terms, let's simplify the expression.

The simplified expression is: $x + 6x^2 + 2$

Conclusion

---

In conclusion, simplifying expressions is a crucial step in solving equations and inequalities. Combining like terms is a fundamental concept in simplifying expressions. By following the steps outlined in this article, we can simplify the given expression: $\left(4x + x^2 - 9\right) + \left(11 - 3x + 5x^2\right)$.

Frequently Asked Questions

---

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms.

Q: What is the coefficient of a term?

A: The coefficient of a term is the number that is multiplied by the variable.

Final Thoughts

---

Simplifying expressions is a crucial step in solving equations and inequalities. By understanding the concept of like terms and how to combine them, we can simplify complex expressions and solve problems more efficiently. In this article, we have provided a step-by-step guide on how to simplify the given expression: $\left(4x + x^2 - 9\right) + \left(11 - 3x + 5x^2\right)$. We hope that this article has provided valuable insights and knowledge on simplifying expressions.

===========================================================

Q&A: Simplifying Expressions and Combining Like Terms

---

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers.

Q: How do I identify like terms in an expression?

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression $2x + 3x + 4y$, the like terms are $2x$ and $3x$.

Q: Can I combine unlike terms?

A: No, unlike terms cannot be combined. They must be left as separate terms in the expression.

Q: What is the coefficient of a term?

A: The coefficient of a term is the number that is multiplied by the variable. For example, in the term $2x$, the coefficient is 2.

Q: How do I combine like terms with different coefficients?

A: To combine like terms with different coefficients, add or subtract the coefficients. For example, in the expression $2x + 3x$, the like terms are $2x$ and $3x$. The combined term is $5x$.

Q: Can I combine like terms with negative coefficients?

A: Yes, you can combine like terms with negative coefficients. For example, in the expression $-2x + 3x$, the like terms are $-2x$ and $3x$. The combined term is $x$.

Q: How do I simplify an expression with multiple like terms?

A: To simplify an expression with multiple like terms, combine the like terms separately and then simplify the resulting expression. For example, in the expression $2x + 3x + 4x + 5y$, the like terms are $2x$, $3x$, and $4x$. The combined term is $9x$. The simplified expression is $9x + 5y$.

Q: Can I simplify an expression with variables raised to different powers?

A: Yes, you can simplify an expression with variables raised to different powers. For example, in the expression $x^2 + 3x + 4$, the like terms are $x^2$ and $3x$. The combined term is $x^2 + 3x$. The simplified expression is $x^2 + 3x + 4$.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, combine the fractions separately and then simplify the resulting expression. For example, in the expression $\frac{1}{2}x + \frac{3}{4}x$, the like terms are $\frac{1}{2}x$ and $\frac{3}{4}x$. The combined term is $\frac{5}{4}x$. The simplified expression is $\frac{5}{4}x$.

Q: Can I simplify an expression with exponents?

A: Yes, you can simplify an expression with exponents. For example, in the expression $x^2 + 3x^2$, the like terms are $x^2$ and $3x^2$. The combined term is $4x^2$. The simplified expression is $4x^2$.

Final Thoughts

---

Simplifying expressions is a crucial step in solving equations and inequalities. By understanding the concept of like terms and how to combine them, we can simplify complex expressions and solve problems more efficiently. In this article, we have provided a comprehensive guide on how to simplify expressions and combine like terms. We hope that this article has provided valuable insights and knowledge on simplifying expressions.