Simplify The Expression: $\[ 7m^2 + 6m - 1 \\]

Feb 26, 2025 by ADMIN 47 views

**Simplifying Algebraic Expressions: A Step-by-Step Guide**

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill for students and professionals alike. In this article, we will focus on simplifying the given expression: $7m^2 + 6m - 1$ . We will break down the process into manageable steps, using a combination of mathematical techniques and logical reasoning.

Understanding the Expression

Before we begin simplifying the expression, let's take a closer look at its components. The expression consists of three terms:

$7m^2$ : This term represents the square of the variable $m$ multiplied by 7.
$6m$ : This term represents the variable $m$ multiplied by 6.
$-1$ : This term is a constant, representing the number -1.

Factoring Out Common Terms

One of the most effective ways to simplify an algebraic expression is to factor out common terms. In this case, we can factor out the greatest common factor (GCF) of the coefficients of the first two terms, which is 1. However, we can also factor out the common factor of the variable $m$ , which is $m$ itself.

import sympy as sp

# Define the variable
m = sp.symbols('m')

# Define the expression
expr = 7*m**2 + 6*m - 1

# Factor out the common term
factored_expr = sp.factor(expr)

print(factored_expr)

Simplifying the Expression

Now that we have factored out the common term, we can simplify the expression further. We can start by combining like terms, which involves adding or subtracting terms that have the same variable and exponent.

import sympy as sp

# Define the variable
m = sp.symbols('m')

# Define the expression
expr = 7*m**2 + 6*m - 1

# Simplify the expression
simplified_expr = sp.simplify(expr)

print(simplified_expr)

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it requires a combination of mathematical techniques and logical reasoning. By factoring out common terms and combining like terms, we can simplify complex expressions and make them more manageable. In this article, we have demonstrated how to simplify the expression $7m^2 + 6m - 1$ using a step-by-step approach.

Final Answer

The final answer is $\boxed{7m^2 + 6m - 1}$ .

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

Frequently Asked Questions

Q: What is the greatest common factor (GCF) of the coefficients of the first two terms?

A: The GCF of the coefficients of the first two terms is 1.

Q: How do I factor out the common term in an algebraic expression?

A: To factor out the common term, identify the common factor of the variable and the coefficients, and multiply it by the remaining terms.

Q: What is the difference between factoring and simplifying an algebraic expression?

A: Factoring involves breaking down an expression into its component parts, while simplifying involves combining like terms and eliminating unnecessary terms.

Q: How do I simplify an algebraic expression using a calculator or computer program?

A: To simplify an algebraic expression using a calculator or computer program, enter the expression into the program and use the simplify function or command.

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

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

Not factoring out common terms
Not combining like terms
Not eliminating unnecessary terms
Not checking for errors in the expression

By following these tips and avoiding common mistakes, you can simplify algebraic expressions with confidence and accuracy.

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a combination of mathematical techniques and logical reasoning. In our previous article, we demonstrated how to simplify the expression $7m^2 + 6m - 1$ using a step-by-step approach. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the greatest common factor (GCF) of the coefficients of the first two terms?

A: The GCF of the coefficients of the first two terms is 1.

Q: How do I factor out the common term in an algebraic expression?

A: To factor out the common term, identify the common factor of the variable and the coefficients, and multiply it by the remaining terms.

Q: What is the difference between factoring and simplifying an algebraic expression?

A: Factoring involves breaking down an expression into its component parts, while simplifying involves combining like terms and eliminating unnecessary terms.

Q: How do I simplify an algebraic expression using a calculator or computer program?

A: To simplify an algebraic expression using a calculator or computer program, enter the expression into the program and use the simplify function or command.

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

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

Not factoring out common terms
Not combining like terms
Not eliminating unnecessary terms
Not checking for errors in the expression

Q: Can I simplify an algebraic expression that has multiple variables?

A: Yes, you can simplify an algebraic expression that has multiple variables by factoring out the common terms and combining like terms.

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

A: To determine if an algebraic expression is already simplified, check if it has been factored out and if like terms have been combined.

Q: Can I use a calculator or computer program to check my work when simplifying an algebraic expression?

A: Yes, you can use a calculator or computer program to check your work when simplifying an algebraic expression.

Q: What is the importance of simplifying algebraic expressions?

A: Simplifying algebraic expressions is important because it helps to:

Make the expression more manageable
Reduce the risk of errors
Improve the accuracy of calculations
Enhance the understanding of mathematical concepts

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a combination of mathematical techniques and logical reasoning. By understanding the concepts and techniques involved in simplifying algebraic expressions, you can improve your mathematical skills and enhance your understanding of mathematical concepts.

Final Answer

The final answer is $\boxed{7m^2 + 6m - 1}$ .

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

Frequently Asked Questions

Q: What is the greatest common factor (GCF) of the coefficients of the first two terms?

A: The GCF of the coefficients of the first two terms is 1.

Q: How do I factor out the common term in an algebraic expression?

A: To factor out the common term, identify the common factor of the variable and the coefficients, and multiply it by the remaining terms.

Q: What is the difference between factoring and simplifying an algebraic expression?

A: Factoring involves breaking down an expression into its component parts, while simplifying involves combining like terms and eliminating unnecessary terms.

Q: How do I simplify an algebraic expression using a calculator or computer program?

A: To simplify an algebraic expression using a calculator or computer program, enter the expression into the program and use the simplify function or command.

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

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

Not factoring out common terms
Not combining like terms
Not eliminating unnecessary terms
Not checking for errors in the expression

By following these tips and avoiding common mistakes, you can simplify algebraic expressions with confidence and accuracy.