Simplify The Expression:${ 4a^2 + 8a^2 - 7a = }$

Mar 11, 2025 by ADMIN 50 views

Simplify the Expression: $4a^2 + 8a^2 - 7a$

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will focus on simplifying the given expression: $4a^2 + 8a^2 - 7a$ . We will break down the expression, apply the rules of algebra, and simplify it to its simplest form.

Understanding the Expression

The given expression is a quadratic expression, which means it contains a squared variable (in this case, $a^2$ ). The expression is: $4a^2 + 8a^2 - 7a$ . To simplify this expression, we need to combine like terms, which means combining terms that have the same variable and exponent.

Combining Like Terms

To combine like terms, we need to identify the terms that have the same variable and exponent. In this case, we have two terms with the variable $a^2$ : $4a^2$ and $8a^2$ . We can combine these two terms by adding their coefficients (the numbers in front of the variable).

# Combining like terms
import sympy as sp
a = sp.symbols('a')

expr = 4a**2 + 8a**2 - 7*a

simplified_expr = sp.simplify(expr)
print(simplified_expr)

Simplifying the Expression

Using the code above, we can simplify the expression by combining like terms. The simplified expression is: $12a^2 - 7a$ .

Factoring Out the Greatest Common Factor (GCF)

Now that we have simplified the expression, we can factor out the greatest common factor (GCF) if possible. In this case, the GCF of $12a^2$ and $-7a$ is $a$ . We can factor out $a$ from both terms:

# Factoring out the GCF
import sympy as sp

a = sp.symbols('a')

expr = 12a**2 - 7a

factored_expr = sp.factor(expr)
print(factored_expr)

Final Simplified Expression

Using the code above, we can factor out the GCF from the expression. The final simplified expression is: $a(12a - 7)$ .

Conclusion

In this article, we simplified the given expression: $4a^2 + 8a^2 - 7a$ . We combined like terms, simplified the expression, and factored out the greatest common factor (GCF) if possible. The final simplified expression is: $a(12a - 7)$ . This expression is in its simplest form, and it cannot be simplified further.

Frequently Asked Questions (FAQs)

Q: What is the simplified expression of $4a^2 + 8a^2 - 7a$ ? A: The simplified expression is: $a(12a - 7)$ .
Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms, simplify the expression, and factor out the greatest common factor (GCF) if possible.
Q: What is the greatest common factor (GCF)? A: The greatest common factor (GCF) is the largest factor that divides all the terms in an expression.

References

[1] Khan Academy. (n.d.). Algebra. Retrieved from https://www.khanacademy.org/math/algebra
[2] Mathway. (n.d.). Algebra. Retrieved from https://www.mathway.com/
[3] Wolfram Alpha. (n.d.). Algebra. Retrieved from https://www.wolframalpha.com/

Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it's essential to understand the rules and techniques involved. In this article, we will provide a comprehensive Q&A section on algebraic expression simplification. We will cover various topics, including combining like terms, simplifying expressions, and factoring out the greatest common factor (GCF).

Q&A Section

Q: What is the simplified expression of $4a^2 + 8a^2 - 7a$ ?

A: The simplified expression is: $a(12a - 7)$ .

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms, simplify the expression, and factor out the greatest common factor (GCF) if possible.

Q: What is the greatest common factor (GCF)?

A: The greatest common factor (GCF) is the largest factor that divides all the terms in an expression.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable and exponent. Then, you can add or subtract the coefficients (the numbers in front of the variable) to simplify the expression.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms involves adding or subtracting the coefficients of terms with the same variable and exponent. Simplifying an expression involves reducing the expression to its simplest form by combining like terms, removing any unnecessary parentheses, and factoring out the greatest common factor (GCF) if possible.

Q: How do I factor out the greatest common factor (GCF)?

A: To factor out the greatest common factor (GCF), you need to identify the GCF of the terms in the expression. Then, you can divide each term by the GCF to simplify the expression.

Q: What is the importance of simplifying algebraic expressions?

A: Simplifying algebraic expressions is essential in mathematics because it helps to:

Reduce the complexity of the expression
Make it easier to solve equations and inequalities
Identify patterns and relationships between variables
Improve problem-solving skills

Q: How do I apply algebraic expression simplification in real-life scenarios?

A: Algebraic expression simplification is used in various real-life scenarios, including:

Physics and engineering: to simplify complex equations and models
Economics: to analyze and predict economic trends
Computer science: to optimize algorithms and data structures
Biology: to model and analyze biological systems

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

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

Failing to combine like terms
Not removing unnecessary parentheses
Not factoring out the greatest common factor (GCF)
Not checking for errors in the expression

Conclusion

In this article, we provided a comprehensive Q&A section on algebraic expression simplification. We covered various topics, including combining like terms, simplifying expressions, and factoring out the greatest common factor (GCF). We also discussed the importance of simplifying algebraic expressions and provided examples of real-life scenarios where algebraic expression simplification is used.

Frequently Asked Questions (FAQs)

Q: What is the simplified expression of $4a^2 + 8a^2 - 7a$ ? A: The simplified expression is: $a(12a - 7)$ .
Q: How do I simplify an algebraic expression? A: To simplify an algebraic expression, you need to combine like terms, simplify the expression, and factor out the greatest common factor (GCF) if possible.
Q: What is the greatest common factor (GCF)? A: The greatest common factor (GCF) is the largest factor that divides all the terms in an expression.

References

[1] Khan Academy. (n.d.). Algebra. Retrieved from https://www.khanacademy.org/math/algebra
[2] Mathway. (n.d.). Algebra. Retrieved from https://www.mathway.com/
[3] Wolfram Alpha. (n.d.). Algebra. Retrieved from https://www.wolframalpha.com/

Simplify The Expression:${ 4a^2 + 8a^2 - 7a = }$

Introduction

Understanding the Expression

Combining Like Terms

Simplifying the Expression

Factoring Out the Greatest Common Factor (GCF)

Final Simplified Expression

Conclusion

Frequently Asked Questions (FAQs)

Further Reading

References

Introduction

Q&A Section

Q: What is the simplified expression of $4a^2 + 8a^2 - 7a$ ?

Q: How do I simplify an algebraic expression?

Q: What is the greatest common factor (GCF)?

Q: How do I combine like terms?

Q: What is the difference between combining like terms and simplifying an expression?

Q: How do I factor out the greatest common factor (GCF)?

Q: What is the importance of simplifying algebraic expressions?

Q: How do I apply algebraic expression simplification in real-life scenarios?

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

Conclusion

Frequently Asked Questions (FAQs)

Further Reading

References

Introduction

Understanding the Expression

Combining Like Terms

Simplifying the Expression

Factoring Out the Greatest Common Factor (GCF)

Final Simplified Expression

Conclusion

Frequently Asked Questions (FAQs)

Further Reading

References

Introduction

Q&A Section

Q: What is the simplified expression of 4a2+8a2−7a4a^2 + 8a^2 - 7a4a2+8a2−7a?

Q: How do I simplify an algebraic expression?

Q: What is the greatest common factor (GCF)?

Q: How do I combine like terms?

Q: What is the difference between combining like terms and simplifying an expression?

Q: How do I factor out the greatest common factor (GCF)?

Q: What is the importance of simplifying algebraic expressions?

Q: How do I apply algebraic expression simplification in real-life scenarios?

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

Conclusion

Frequently Asked Questions (FAQs)

Further Reading

References

Q: What is the simplified expression of $4a^2 + 8a^2 - 7a$ ?