Given The Functions:$\[ \begin{array}{l} f(x) = 3x + 5 \\ g(x) = 4x^2 - 2 \\ h(x) = X^2 - 3x + 1 \end{array} \\]Find \[$ F(x) + G(x) - H(x) \$\].Options:A. \[$ 3x^2 + 2 \$\]B. \[$ 6x^2 + 6x - 1 \$\]C. \[$ 5x^2 +

In mathematics, algebraic expressions are a fundamental concept that plays a crucial role in various mathematical operations. When dealing with algebraic expressions, it's essential to understand how to simplify them to make calculations easier and more manageable. In this article, we will explore how to simplify algebraic expressions by combining like terms and applying basic algebraic operations.

Understanding the Given Functions

Before we dive into simplifying the given expression, let's take a closer look at the functions provided:

${ f(x) = 3x + 5 }$ ${ g(x) = 4x^2 - 2 }$ ${ h(x) = x^2 - 3x + 1 }$

These functions are polynomial expressions, which are a combination of variables and coefficients. To simplify the given expression, we will need to combine like terms and apply basic algebraic operations.

Simplifying the Expression

The given expression is:

${ f(x) + g(x) - h(x) }$

To simplify this expression, we will need to substitute the given functions and then combine like terms.

${ f(x) + g(x) - h(x) = (3x + 5) + (4x^2 - 2) - (x^2 - 3x + 1) }$

Now, let's simplify the expression by combining like terms:

${ (3x + 5) + (4x^2 - 2) - (x^2 - 3x + 1) }$

${ = 3x + 5 + 4x^2 - 2 - x^2 + 3x - 1 }$

${ = 3x + 5 + 4x^2 - x^2 - 2 + 3x - 1 }$

${ = 3x + 3x + 5 - 2 - 1 + 4x^2 - x^2 }$

${ = 6x + 2 + 3x^2 }$

${ = 3x^2 + 6x + 2 }$

Comparing the Simplified Expression with the Options

Now that we have simplified the expression, let's compare it with the given options:

A. ${ 3x^2 + 2 }$ B. ${ 6x^2 + 6x - 1 }$ C. ${ 5x^2 + 6x + 2 }$

Based on our simplified expression, we can see that the correct answer is:

C. ${ 3x^2 + 6x + 2 }$

Conclusion

In this article, we explored how to simplify algebraic expressions by combining like terms and applying basic algebraic operations. We took a closer look at the given functions and simplified the expression by substituting the functions and combining like terms. Finally, we compared the simplified expression with the given options and determined the correct answer.

Key Takeaways

• Algebraic expressions are a fundamental concept in mathematics that plays a crucial role in various mathematical operations.
• To simplify algebraic expressions, we need to combine like terms and apply basic algebraic operations.
• When dealing with polynomial expressions, we need to be careful when combining like terms to avoid errors.
• Simplifying algebraic expressions can make calculations easier and more manageable.

Frequently Asked Questions

• Q: What is an algebraic expression? A: An algebraic expression is a combination of variables and coefficients that can be simplified using basic algebraic operations.
• Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms and apply basic algebraic operations.
• Q: What is the difference between a polynomial expression and an algebraic expression? A: A polynomial expression is a specific type of algebraic expression that consists of variables and coefficients raised to non-negative integer powers.
  Algebraic Expressions: A Q&A Guide =====================================

In our previous article, we explored how to simplify algebraic expressions by combining like terms and applying basic algebraic operations. In this article, we will continue to delve deeper into the world of algebraic expressions and answer some frequently asked questions.

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables and coefficients that can be simplified using basic algebraic operations. Algebraic expressions can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Q: What is the difference between a polynomial expression and an algebraic expression?

A: A polynomial expression is a specific type of algebraic expression that consists of variables and coefficients raised to non-negative integer powers. In other words, a polynomial expression is an algebraic expression that can be written in the form:

${ ax^n + bx^{n-1} + \ldots + cx + d }$

where a, b, c, and d are constants, and x is the variable.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and apply basic algebraic operations. Here are the steps to simplify an algebraic expression:

1. Identify the like terms in the expression.
2. Combine the like terms by adding or subtracting their coefficients.
3. Apply basic algebraic operations such as multiplication and division to simplify the expression.

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

A: The order of operations in algebraic expressions is a set of rules that dictate the order in which mathematical operations should be performed. 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 evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values for the variables and then simplify the expression using the order of operations.

Q: What is the difference between an equation and an expression?

A: An equation is a statement that two expressions are equal, while an expression is a combination of variables and coefficients that can be simplified using basic algebraic operations. In other words, an equation is a statement that can be written in the form:

${ a = b }$

where a and b are expressions.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable on one side of the equation and then simplify the expression. Here are the steps to solve an equation:

1. Simplify the equation by combining like terms.
2. Isolate the variable on one side of the equation.
3. Simplify the expression to find the value of the variable.

Q: What is the importance of algebraic expressions in real-life applications?

A: Algebraic expressions are used in a wide range of real-life applications, including:

• Physics: Algebraic expressions are used to describe the motion of objects and the behavior of physical systems.
• Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and buildings.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future economic trends.
• Computer Science: Algebraic expressions are used to develop algorithms and solve complex problems.

Conclusion

In this article, we have answered some frequently asked questions about algebraic expressions and provided a comprehensive guide to simplifying and evaluating algebraic expressions. We have also discussed the importance of algebraic expressions in real-life applications and provided examples of how they are used in various fields.

Key Takeaways

• Algebraic expressions are a fundamental concept in mathematics that plays a crucial role in various mathematical operations.
• To simplify an algebraic expression, you need to combine like terms and apply basic algebraic operations.
• The order of operations in algebraic expressions is a set of rules that dictate the order in which mathematical operations should be performed.
• Algebraic expressions are used in a wide range of real-life applications, including physics, engineering, economics, and computer science.

Frequently Asked Questions

• Q: What is an algebraic expression? A: An algebraic expression is a combination of variables and coefficients that can be simplified using basic algebraic operations.
• Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms and apply basic algebraic operations.
• Q: What is the order of operations in algebraic expressions? A: The order of operations in algebraic expressions is a set of rules that dictate the order in which mathematical operations should be performed.
• Q: How do I evaluate an algebraic expression? A: To evaluate an algebraic expression, you need to substitute the given values for the variables and then simplify the expression using the order of operations.