Simplify The Expression: 4 X + 7 Y + 8 X − 2 Y 4x + 7y + 8x - 2y 4 X + 7 Y + 8 X − 2 Y

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying the given expression: $4x + 7y + 8x - 2y$. We will use basic algebraic properties and techniques to simplify the expression and arrive at the final result.

Understanding the Expression

The given expression is a linear combination of two variables, x and y. It consists of four terms: $4x$, $7y$, $8x$, and $-2y$. To simplify the expression, we need to combine like terms, which are terms that have the same variable raised to the same power.

Combining Like Terms

To combine like terms, we need to identify the terms that have the same variable raised to the same power. In this case, we have two terms with the variable x: $4x$ and $8x$. We also have two terms with the variable y: $7y$ and $-2y$.

Combining Terms with the Variable x

We can combine the two terms with the variable x by adding their coefficients. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficient of $4x$ is 4, and the coefficient of $8x$ is 8.

# Define the coefficients of the terms with the variable x
coefficient_1 = 4
coefficient_2 = 8
coefficient_x = coefficient_1 + coefficient_2
print(coefficient_x)

The output of the code above is 12. Therefore, the combined term with the variable x is $12x$.

Combining Terms with the Variable y

We can combine the two terms with the variable y by adding their coefficients. The coefficient of $7y$ is 7, and the coefficient of $-2y$ is -2.

# Define the coefficients of the terms with the variable y
coefficient_1 = 7
coefficient_2 = -2

coefficient_y = coefficient_1 + coefficient_2
print(coefficient_y)

The output of the code above is 5. Therefore, the combined term with the variable y is $5y$.

Simplifying the Expression

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

# Define the combined terms
term_x = "12x"
term_y = "5y"

simplified_expression = term_x + " + " + term_y
print(simplified_expression)

The output of the code above is $12x + 5y$. Therefore, the simplified expression is $12x + 5y$.

Conclusion

In this article, we simplified the given expression: $4x + 7y + 8x - 2y$. We used basic algebraic properties and techniques to combine like terms and arrive at the final result. The simplified expression is $12x + 5y$. This result can be used in a variety of mathematical applications, such as solving systems of linear equations and graphing linear functions.

Final Answer

The final answer is $\boxed{12x + 5y}$.

Related Topics

• Simplifying algebraic expressions
• Combining like terms
• Solving systems of linear equations
• Graphing linear functions

References

• Algebraic Expressions
• Combining Like Terms
• Solving Systems of Linear Equations
• Graphing Linear Functions
  

Introduction

In our previous article, we simplified the given expression: $4x + 7y + 8x - 2y$. We used basic algebraic properties and techniques to combine like terms and arrive at the final result. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $4x$ and $8x$ are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add their coefficients. The coefficient of a term is the number that is multiplied by the variable. For example, to combine $4x$ and $8x$, you would add their coefficients: $4 + 8 = 12$. Therefore, the combined term is $12x$.

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

A: A coefficient is a number that is multiplied by a variable, while a constant is a number that is not multiplied by a variable. For example, in the term $4x$, 4 is the coefficient and x is the variable. In the term 5, 5 is the constant.

Q: Can I simplify an expression with more than two variables?

A: Yes, you can simplify an expression with more than two variables. You need to combine like terms, which are terms that have the same variable raised to the same power. For example, to simplify the expression $2x + 3y + 4x - 2y$, you would combine the like terms: $2x + 4x = 6x$ and $3y - 2y = y$.

Q: How do I know if an expression is already simplified?

A: An expression is already simplified if there are no like terms that can be combined. For example, the expression $2x + 3y$ is already simplified because there are no like terms that can be combined.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients. You need to combine like terms, which are terms that have the same variable raised to the same power. For example, to simplify the expression $-2x + 3y - 4x + 2y$, you would combine the like terms: $-2x - 4x = -6x$ and $3y + 2y = 5y$.

Conclusion

In this article, we answered some frequently asked questions related to simplifying algebraic expressions. We covered topics such as like terms, combining like terms, coefficients, constants, and simplifying expressions with more than two variables. We hope that this article has been helpful in clarifying any doubts you may have had about simplifying algebraic expressions.

Final Answer

The final answer is $\boxed{12x + 5y}$.

Related Topics

• Simplifying algebraic expressions
• Combining like terms
• Solving systems of linear equations
• Graphing linear functions

References

• Algebraic Expressions
• Combining Like Terms
• Solving Systems of Linear Equations
• Graphing Linear Functions