Simplify The Expression: 40 M 2 70 M − 30 \frac{40 M^2}{70 M-30} 70 M − 30 40 M 2 ​ A. 1 M + 6 \frac{1}{m+6} M + 6 1 ​ B. 7 M − 5 4 \frac{7 M-5}{4} 4 7 M − 5 ​ C. 4 7 M − 5 \frac{4}{7 M-5} 7 M − 5 4 ​ D. 4 M 2 7 M − 3 \frac{4 M^2}{7 M-3} 7 M − 3 4 M 2 ​

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the underlying concepts. In this article, we will focus on simplifying the given expression 40m270m−30\frac{40 m^2}{70 m-30} using various techniques and strategies. We will explore different methods to simplify the expression and arrive at the final answer.

Factorization

The first step in simplifying the expression is to factorize the numerator and denominator. Factorization involves breaking down an expression into its simplest form by identifying common factors.

import sympy as sp

m = sp.symbols('m')



expr = (40m**2) / (70m - 30)



numerator = sp.factor(40m**2)
denominator = sp.factor(70m - 30)


print("Numerator:", numerator)
print("Denominator:", denominator)

Canceling Common Factors

After factorizing the numerator and denominator, we can cancel out any common factors. This involves dividing both the numerator and denominator by the common factor.

# Cancel out common factors
simplified_expr = sp.cancel(expr)

print("Simplified Expression:", simplified_expr)

Simplifying the Expression

Now that we have canceled out the common factors, we can simplify the expression further by combining like terms.

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

print("Final Expression:", final_expr)

Conclusion

In this article, we have simplified the expression 40m270m−30\frac{40 m^2}{70 m-30} using factorization and canceling common factors. We have also combined like terms to arrive at the final answer. The simplified expression is 4m27m−5\frac{4m^2}{7m-5}.

Final Answer

The final answer is 4m27m−5\boxed{\frac{4m^2}{7m-5}}.

Discussion

The expression 40m270m−30\frac{40 m^2}{70 m-30} can be simplified using various techniques and strategies. In this article, we have used factorization and canceling common factors to simplify the expression. We have also combined like terms to arrive at the final answer.

Common Mistakes

When simplifying algebraic expressions, it is essential to avoid common mistakes. Some common mistakes include:

  • Not canceling out common factors
  • Not combining like terms
  • Not using the correct order of operations

Tips and Tricks

To simplify algebraic expressions effectively, follow these tips and tricks:

  • Factorize the numerator and denominator
  • Cancel out common factors
  • Combine like terms
  • Use the correct order of operations

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. Some examples include:

  • Simplifying complex equations in physics and engineering
  • Solving optimization problems in economics and finance
  • Modeling population growth in biology and ecology

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics. By using factorization and canceling common factors, we can simplify complex expressions and arrive at the final answer. The expression 40m270m−30\frac{40 m^2}{70 m-30} can be simplified using various techniques and strategies, and the final answer is 4m27m−5\frac{4m^2}{7m-5}.

Introduction

In our previous article, we simplified the expression 40m270m−30\frac{40 m^2}{70 m-30} using factorization and canceling common factors. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Q&A

Q1: What is the first step in simplifying an algebraic expression?

A1: The first step in simplifying an algebraic expression is to factorize the numerator and denominator.

Q2: How do I factorize an algebraic expression?

A2: To factorize an algebraic expression, you need to identify the common factors in the numerator and denominator. You can use the distributive property to factorize the expression.

Q3: What is the distributive property?

A3: The distributive property is a mathematical concept that states that a single term can be distributed to multiple terms. For example, a(b+c)=ab+aca(b+c) = ab + ac.

Q4: How do I cancel out common factors?

A4: To cancel out common factors, you need to divide both the numerator and denominator by the common factor.

Q5: What is the difference between simplifying and canceling?

A5: Simplifying an algebraic expression involves combining like terms and using the correct order of operations. Canceling involves dividing both the numerator and denominator by a common factor.

Q6: How do I know when to simplify and when to cancel?

A6: You should simplify an algebraic expression when there are like terms that can be combined. You should cancel when there are common factors that can be divided out.

Q7: What are some common mistakes to avoid when simplifying algebraic expressions?

A7: Some common mistakes to avoid when simplifying algebraic expressions include not canceling out common factors, not combining like terms, and not using the correct order of operations.

Q8: How do I use the correct order of operations?

A8: To use the correct order of operations, you need to follow the PEMDAS rule: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q9: What are some real-world applications of simplifying algebraic expressions?

A9: Some real-world applications of simplifying algebraic expressions include simplifying complex equations in physics and engineering, solving optimization problems in economics and finance, and modeling population growth in biology and ecology.

Q10: How can I practice simplifying algebraic expressions?

A10: You can practice simplifying algebraic expressions by working through example problems and exercises. You can also use online resources and tools to help you practice.

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics. By following the steps outlined in this article, you can simplify complex expressions and arrive at the final answer. Remember to factorize, cancel, and combine like terms to simplify algebraic expressions.

Final Answer

The final answer is 4m27m−5\boxed{\frac{4m^2}{7m-5}}.

Discussion

The expression 40m270m−30\frac{40 m^2}{70 m-30} can be simplified using various techniques and strategies. In this article, we have answered some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Common Mistakes

When simplifying algebraic expressions, it is essential to avoid common mistakes. Some common mistakes include:

  • Not canceling out common factors
  • Not combining like terms
  • Not using the correct order of operations

Tips and Tricks

To simplify algebraic expressions effectively, follow these tips and tricks:

  • Factorize the numerator and denominator
  • Cancel out common factors
  • Combine like terms
  • Use the correct order of operations

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. Some examples include:

  • Simplifying complex equations in physics and engineering
  • Solving optimization problems in economics and finance
  • Modeling population growth in biology and ecology

Conclusion

In conclusion, simplifying algebraic expressions is a crucial skill in mathematics. By following the steps outlined in this article, you can simplify complex expressions and arrive at the final answer. Remember to factorize, cancel, and combine like terms to simplify algebraic expressions.