Add The Following Expression: X^2+\left(4 X^2+9 X+3\right ]

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will focus on simplifying a specific expression: $x^2+\left(4 x^2+9 x+3\right)$. We will break down the expression into smaller parts, apply the rules of algebra, and finally simplify the expression to its simplest form.

Understanding the Expression

The given expression is a combination of two terms: $x^2$ and $\left(4 x^2+9 x+3\right)$. To simplify this expression, we need to understand the rules of algebra, particularly the distributive property and the order of operations.

Distributive Property

The distributive property states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$$a(b+c) = ab + ac$$

This property allows us to distribute a single term across the terms inside the parentheses.

Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

Now that we have a good understanding of the distributive property and the order of operations, let's simplify the expression:

$$x^2+\left(4 x^2+9 x+3\right)$$

To simplify this expression, we need to apply the distributive property and the order of operations.

Step 1: Distribute the Term Inside the Parentheses

Using the distributive property, we can distribute the term $x^2$ across the terms inside the parentheses:

$$x^2+\left(4 x^2+9 x+3\right) = x^2 + 4x^2 + 9x + 3$$

Step 2: Combine Like Terms

Now that we have distributed the term inside the parentheses, we can combine like terms. Like terms are terms that have the same variable raised to the same power.

In this case, we have two like terms: $x^2$ and $4x^2$. We can combine these terms by adding their coefficients:

$$x^2 + 4x^2 = 5x^2$$

So, the expression becomes:

$$5x^2 + 9x + 3$$

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression further. We can rewrite the expression as:

$$5x^2 + 9x + 3 = 5x^2 + 9x + 3$$

This is the simplest form of the expression.

Conclusion

In this article, we simplified the expression $x^2+\left(4 x^2+9 x+3\right)$ using the distributive property and the order of operations. We broke down the expression into smaller parts, applied the rules of algebra, and finally simplified the expression to its simplest form. This process helps us understand the rules of algebra and how to simplify complex expressions.

Final Answer

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Introduction

In our previous article, we simplified the expression $x^2+\left(4 x^2+9 x+3\right)$ using the distributive property and the order of operations. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a rule in algebra that allows us to distribute a single term across the terms inside the parentheses. It states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$$a(b+c) = ab + ac$$

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

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

A: To simplify an expression with multiple terms, you need to follow these steps:

1. Distribute the term inside the parentheses using the distributive property.
2. Combine like terms by adding or subtracting their coefficients.
3. Simplify the expression further by rewriting it in a simpler form.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $x^2$ and $4x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I know which terms to combine?

A: To combine like terms, you need to look for terms that have the same variable raised to the same power. For example, in the expression $x^2 + 4x^2 + 9x + 3$, you can combine the terms $x^2$ and $4x^2$ because they are like terms.

Q: Can I simplify an expression with variables and constants?

A: Yes, you can simplify an expression with variables and constants. To do this, you need to follow the same steps as before: distribute the term inside the parentheses, combine like terms, and simplify the expression further.

Q: What if I have an expression with multiple parentheses?

A: If you have an expression with multiple parentheses, you need to evaluate the expressions inside the parentheses from left to right. For example, in the expression $(x^2 + 4x^2) + (9x + 3)$, you need to evaluate the expressions inside the parentheses first, and then combine like terms.

Conclusion

In this article, we answered some frequently asked questions about simplifying algebraic expressions. We covered topics such as the distributive property, the order of operations, and like terms. We also provided examples of how to simplify expressions with multiple terms, variables, and constants.

Final Tips

• Always follow the order of operations when simplifying expressions.
• Look for like terms and combine them by adding or subtracting their coefficients.
• Simplify the expression further by rewriting it in a simpler form.
• Practice, practice, practice! The more you practice simplifying expressions, the more comfortable you will become with the rules of algebra.

Common Mistakes

• Failing to distribute the term inside the parentheses.
• Failing to combine like terms.
• Not following the order of operations.
• Not simplifying the expression further.

Final Answer

The final answer is: Simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. By following the distributive property, the order of operations, and combining like terms, we can simplify complex expressions and solve problems with ease.