Find The Sum.$\left(13x^2 + 5x\right) + 8x^2 =$A. $26x^2$ B. $26x^5$ C. $20x^2 + 5x$ D. $21x^2 + 5x$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on finding the sum of two algebraic expressions and simplifying the resulting expression. We will use a step-by-step approach to make the process easier to understand and follow.

Understanding Algebraic Expressions

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Variables are represented by letters, such as x or y, and constants are numbers. Mathematical operations include addition, subtraction, multiplication, and division.

The Problem

The problem we will be solving is: $\left(13x^2 + 5x\right) + 8x^2 =$ A. $26x^2$ B. $26x^5$ C. $20x^2 + 5x$ D. $21x^2 + 5x$

Step 1: Distribute the Parentheses

To simplify the expression, we need to distribute the parentheses. This means that we need to multiply each term inside the parentheses by the term outside the parentheses.

$\left(13x^2 + 5x\right) + 8x^2 = 13x^2 + 5x + 8x^2$

Step 2: Combine Like Terms

Now that we have distributed the parentheses, we can combine like terms. Like terms are terms that have the same variable and exponent. In this case, we have two terms with the variable x^2.

$13x^2 + 5x + 8x^2 = 13x^2 + 8x^2 + 5x$

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by adding the coefficients of the like terms.

$13x^2 + 8x^2 = 21x^2$

So, the simplified expression is: $21x^2 + 5x$

Conclusion

In this article, we have learned how to simplify an algebraic expression by distributing the parentheses and combining like terms. We have also seen how to add coefficients of like terms to simplify the expression. The final answer to the problem is: $21x^2 + 5x$

Tips and Tricks

• When distributing the parentheses, make sure to multiply each term inside the parentheses by the term outside the parentheses.
• When combining like terms, make sure to add the coefficients of the like terms.
• When simplifying the expression, make sure to combine like terms and add coefficients.

Common Mistakes

• Not distributing the parentheses correctly.
• Not combining like terms correctly.
• Not adding coefficients correctly.

Real-World Applications

Simplifying algebraic expressions is a crucial skill in many real-world applications, such as:

• Physics: Simplifying algebraic expressions is essential in physics to solve problems involving motion, energy, and momentum.
• Engineering: Simplifying algebraic expressions is essential in engineering to design and analyze complex systems.
• Computer Science: Simplifying algebraic expressions is essential in computer science to optimize algorithms and data structures.

Final Thoughts

Introduction

In our previous article, we discussed how to simplify algebraic expressions by distributing the parentheses and combining like terms. In this article, we will provide a Q&A guide to help you understand and apply the concepts of simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Variables are represented by letters, such as x or y, and constants are numbers. Mathematical operations include addition, subtraction, multiplication, and division.

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

A: A variable is a letter that represents a value that can change, while a constant is a number that does not change.

Q: How do I distribute the parentheses in an algebraic expression?

A: To distribute the parentheses, you need to multiply each term inside the parentheses by the term outside the parentheses. For example, if you have the expression (2x + 3) + 4x, you would distribute the parentheses by multiplying each term inside the parentheses by 4x.

(2x + 3) + 4x = 2x(4x) + 3(4x) + 4x

Q: How do I combine like terms in an algebraic expression?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the expression 2x + 3x, you would combine the like terms by adding the coefficients.

2x + 3x = 5x

Q: What is the order of operations in algebraic expressions?

A: The order of operations in algebraic expressions 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 algebraic expression with multiple variables?

A: To simplify an algebraic expression with multiple variables, you need to follow the same steps as before: distribute the parentheses, combine like terms, and add coefficients. For example, if you have the expression (2x + 3y) + 4x, you would distribute the parentheses and combine like terms.

(2x + 3y) + 4x = 2x(4x) + 3y(4x) + 4x

Combine like terms:

2x(4x) + 4x = 8x^2 + 4x

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not distributing the parentheses correctly.
• Not combining like terms correctly.
• Not adding coefficients correctly.
• Not following the order of operations.

Q: How do I apply simplifying algebraic expressions to real-world problems?

A: Simplifying algebraic expressions is a crucial skill in many real-world applications, such as:

• Physics: Simplifying algebraic expressions is essential in physics to solve problems involving motion, energy, and momentum.
• Engineering: Simplifying algebraic expressions is essential in engineering to design and analyze complex systems.
• Computer Science: Simplifying algebraic expressions is essential in computer science to optimize algorithms and data structures.

Conclusion

Simplifying algebraic expressions is a fundamental concept in mathematics, and it requires practice and patience to master. By following the steps outlined in this article, you can simplify algebraic expressions with ease. Remember to distribute the parentheses, combine like terms, and add coefficients to simplify the expression. With practice and patience, you can become proficient in simplifying algebraic expressions and apply it to real-world problems.