58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6. In the realm of algebra, expressions serve as fundamental building blocks to model and understand various mathematical concepts. One such expression that often confuses students is “2x^2 – 9x^2; 5 – 3x + y + 6.” In this article, we will delve into this expression, break it down, simplify each part, and finally, solve it step by step. By the end, you’ll have a clear understanding of the expression and its applications.

Table of Contents

## Understanding the Expression: 58.2x^2 – 9x^2; 5 – 3x + y + 6

Before we start simplifying the given expression, let’s take a moment to understand its structure. The expression is composed of two parts separated by a semicolon. The first part is “2x^2 – 9x^2,” and the second part is “5 – 3x + y + 6.”

## Breaking Down the Expression

### Part 1: 2x^2 – 9x^2

In this section, we will focus on the first part of the expression, “2x^2 – 9x^2.” The expression consists of two terms: “2x^2” and “-9x^2.” Both terms contain variables (x) raised to the power of 2.

### Part 2: 5 – 3x + y + 6

Now, we move on to the second part of the expression, “5 – 3x + y + 6.” This part also contains multiple terms: “5,” “-3x,” “y,” and “6.” Each term has its coefficient and variables.

## Simplifying Each Part of the Expression

### Part 1: Simplifying 2x^2 – 9x^2

To simplify the first part, we need to combine the like terms. Both terms have the same variable (x) raised to the power of 2. When we combine “2x^2” and “-9x^2,” we get “-7x^2.”

### Part 2: Simplifying 5 – 3x + y + 6

In this section, we’ll simplify the second part of the expression. There are no like terms to combine, so we keep the terms as they are.

## Combining the Simplified Parts

Now that we have simplified both parts, we can combine them back together. The simplified expression is “-7x^2; 5 – 3x + y + 6.”

## Solving the Expression

To solve the expression, we need to provide a specific value for the variable (x) and evaluate the expression based on that value. Let’s take an example:

Suppose we have x = 3; now, let’s find the value of the expression:

-7(3)^2; 5 – 3(3) + y + 6 = -7(9); 5 – 9 + y + 6 = -63; -4 + y + 6 = -63; 2 + y

## Practical Applications of Algebraic Expressions

Algebraic expressions find widespread applications in various fields, including physics, engineering, economics, and computer science. They are used to model and solve real-world problems, analyze data, and make predictions. Understanding algebraic expressions is crucial for advancing in these domains.

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## Conclusion

In conclusion, the algebraic expression “2x^2 – 9x^2; 5 – 3x + y + 6” may appear complex at first glance, but by breaking it down, simplifying each part, and combining them back together, we can gain a better understanding of its structure. Furthermore, solving the expression for specific values of the variable helps us evaluate its numerical value in different scenarios. Algebraic expressions hold significant importance in practical applications, making them a vital topic to grasp in mathematics.