Find The Sum: $\left(3x^2 + 2x + 3\right) + \left(x^2 + X + 1\right$\]A. $4x^2 + 3x + 4$ B. $4x^4 + 4x + 4$ C. $3x^2 + 4x + 4$ D. $3x^4 + 3x + 4$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill to master. In this article, we will focus on finding the sum of two algebraic expressions, which is a crucial operation in algebra. We will use a step-by-step approach to simplify the given expressions and arrive at the correct answer.

The Problem

The problem requires us to find the sum of two algebraic expressions:

$\left(3x^2 + 2x + 3\right) + \left(x^2 + x + 1\right)$

Step 1: Identify the Like Terms

To simplify the given expressions, we need to identify the like terms. Like terms are the terms that have the same variable and exponent. In this case, the like terms are:

• $3x^2$ and $x^2$
• $2x$ and $x$
• $3$ and $1$

Step 2: Combine the Like Terms

Now that we have identified the like terms, we can combine them by adding their coefficients. The coefficients are the numbers that are multiplied by the variables.

• $3x^2 + x^2 = 4x^2$
• $2x + x = 3x$
• $3 + 1 = 4$

Step 3: Write the Simplified Expression

Now that we have combined the like terms, we can write the simplified expression:

$4x^2 + 3x + 4$

Conclusion

In this article, we have simplified the given algebraic expressions by identifying the like terms and combining them. The final answer is:

$4x^2 + 3x + 4$

This is the correct answer, and it can be verified by adding the two original expressions:

$\left(3x^2 + 2x + 3\right) + \left(x^2 + x + 1\right) = 4x^2 + 3x + 4$

Answer Key

The correct answer is:

A. $4x^2 + 3x + 4$

Discussion

This problem requires a basic understanding of algebraic expressions and the ability to identify and combine like terms. It is an essential skill for students to master in order to solve more complex problems in algebra.

Tips and Tricks

• When simplifying algebraic expressions, it is essential to identify the like terms and combine them.
• Use the distributive property to expand the expressions and make it easier to identify the like terms.
• Check your work by adding the original expressions to verify the answer.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, such as:

• Calculating the area and perimeter of shapes
• Finding the volume of solids
• Solving systems of equations
• Modeling real-world problems using algebraic expressions

Conclusion

Introduction

In our previous article, we discussed how to simplify algebraic expressions by identifying and combining like terms. In this article, we will provide a Q&A guide to help students understand the concept better and practice their skills.

Q: What are like terms?

A: Like terms are the terms that have the same variable and exponent. For example, $3x^2$ and $x^2$ are like terms because they both have the variable $x$ and the exponent $2$.

Q: How do I identify like terms?

A: To identify like terms, you need to look for the terms that have the same variable and exponent. You can also use the distributive property to expand the expressions and make it easier to identify the like terms.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows you to expand an expression by multiplying each term inside the parentheses by a factor. For example, $a(b + c) = ab + ac$.

Q: How do I combine like terms?

A: To combine like terms, you need to add their coefficients. The coefficients are the numbers that are multiplied by the variables. For example, $3x^2 + x^2 = 4x^2$ because the coefficients of $x^2$ are $3$ and $1$, which add up to $4$.

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable, while a variable is a letter or symbol that represents a value. For example, in the expression $3x^2$, $3$ is the coefficient and $x^2$ is the variable.

Q: Can I simplify an expression with variables of different exponents?

A: No, you cannot simplify an expression with variables of different exponents. For example, $x^2 + x$ cannot be simplified because the variables have different exponents.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to find a common denominator and then combine the fractions. For example, $\frac{1}{2}x + \frac{1}{3}x = \frac{3}{6}x + \frac{2}{6}x = \frac{5}{6}x$.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients. For example, $-3x^2 + 2x^2 = -x^2$ because the coefficients are $-3$ and $2$, which add up to $-1$.

Q: How do I check my work?

A: To check your work, you need to add the original expressions to verify the answer. For example, if you simplified the expression $3x^2 + 2x + 3$ to $4x^2 + 3x + 4$, you need to add the original expression to the simplified expression to verify that the answer is correct.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By identifying and combining like terms, we can simplify complex expressions and arrive at the correct answer. This Q&A guide provides a comprehensive overview of the concept and helps students practice their skills.

Practice Problems

1. Simplify the expression $2x^2 + 3x + 1$.
2. Simplify the expression $x^2 + 2x + 3$.
3. Simplify the expression $-2x^2 + 3x - 1$.
4. Simplify the expression $\frac{1}{2}x + \frac{1}{3}x$.
5. Simplify the expression $-3x^2 + 2x^2$.

Answer Key

1. $2x^2 + 3x + 1$
2. $x^2 + 2x + 3$
3. $-2x^2 + 3x - 1$
4. $\frac{5}{6}x$
5. $-x^2$