Rewrite In Simplest Terms: Left Parenthesis, Minus, 10, X, Plus, 4, Y, Right Parenthesis, Minus, Left Parenthesis, 4, X, Minus, 10, Y, Right Parenthesis(−10x+4y)−(4x−10y)

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying a specific algebraic expression: (−10x+4y)−(4x−10y). We will break down the expression into smaller parts, apply the rules of algebra, and finally arrive at the simplified form.

Understanding the Expression

The given expression is a combination of two algebraic expressions, each enclosed in parentheses. The first expression is −10x+4y, and the second expression is 4x−10y. To simplify the given expression, we need to apply the rules of algebra, specifically the distributive property and the rule for subtracting a negative number.

Step 1: Apply the Distributive Property

The distributive property states that for any real numbers a, b, and c, a(b+c) = ab + ac. We can apply this property to the given expression by distributing the negative sign to the terms inside the second parentheses.

(−10x+4y)−(4x−10y) = −10x+4y−4x+10y

Step 2: Combine Like Terms

Now that we have applied the distributive property, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable x and two terms with the variable y.

−10x+4y−4x+10y = −10x−4x+4y+10y

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by combining the coefficients of the variables. The coefficient of a term is the number that multiplies the variable.

−10x−4x+4y+10y = −14x+14y

Conclusion

In this article, we have simplified the algebraic expression (−10x+4y)−(4x−10y) by applying the distributive property and combining like terms. The simplified expression is −14x+14y. This expression can be further simplified by factoring out the greatest common factor (GCF) of the coefficients, which is 14.

Final Answer

The final answer is:

−14x+14y\boxed{−14x+14y}

Tips and Tricks

  • When simplifying algebraic expressions, always start by applying the distributive property.
  • Combine like terms by adding or subtracting the coefficients of the variables.
  • Simplify the expression by combining the coefficients of the variables.
  • Factor out the greatest common factor (GCF) of the coefficients to further simplify the expression.

Common Mistakes

  • Failing to apply the distributive property when simplifying algebraic expressions.
  • Not combining like terms when simplifying algebraic expressions.
  • Not simplifying the expression by combining the coefficients of the variables.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, algebraic expressions are used to describe the motion of objects, while in engineering, they are used to design and optimize systems. In economics, algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

Introduction

In our previous article, we explored the process of simplifying algebraic expressions, focusing on the expression (−10x+4y)−(4x−10y). We applied the distributive property and combined like terms to arrive at the simplified expression −14x+14y. In this article, we will address some common questions and concerns related to simplifying algebraic expressions.

Q&A

Q: What is the distributive property, and how is it used in simplifying algebraic expressions?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers a, b, and c, a(b+c) = ab + ac. When simplifying algebraic expressions, we use the distributive property to distribute the negative sign to the terms inside the second parentheses.

Q: How do I identify like terms in an algebraic expression?

A: Like terms are terms that have the same variable raised to the same power. To identify like terms, look for terms with the same variable and exponent. For example, in the expression 2x + 3x, the terms 2x and 3x are like terms because they both have the variable x raised to the power of 1.

Q: Can I simplify an algebraic expression by combining like terms if the terms are not directly next to each other?

A: Yes, you can simplify an algebraic expression by combining like terms even if the terms are not directly next to each other. For example, in the expression 2x + 3y + 4x, you can combine the like terms 2x and 4x to get 6x.

Q: What is the greatest common factor (GCF), and how is it used in simplifying algebraic expressions?

A: The greatest common factor (GCF) is the largest number that divides all the coefficients of the terms in an algebraic expression. When simplifying algebraic expressions, we can factor out the GCF to simplify the expression further.

Q: Can I simplify an algebraic expression by canceling out terms?

A: No, you cannot simplify an algebraic expression by canceling out terms. Canceling out terms is not a valid operation in algebra. Instead, you can combine like terms or factor out the GCF to simplify the expression.

Q: How do I know when to stop simplifying an algebraic expression?

A: You can stop simplifying an algebraic expression when you have combined all the like terms and factored out the GCF. At this point, the expression is in its simplest form.

Q: Can I use a calculator to simplify algebraic expressions?

A: Yes, you can use a calculator to simplify algebraic expressions. However, it's essential to understand the underlying math concepts and be able to simplify expressions manually.

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 apply the distributive property
  • Not combining like terms
  • Not simplifying the expression by combining the coefficients of the variables
  • Canceling out terms

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By understanding the distributive property, identifying like terms, and combining coefficients, we can simplify complex expressions and arrive at a more manageable form. We hope that this Q&A guide has provided a clear and concise overview of the process of simplifying algebraic expressions.

Tips and Tricks

  • Always start by applying the distributive property when simplifying algebraic expressions.
  • Combine like terms by adding or subtracting the coefficients of the variables.
  • Simplify the expression by combining the coefficients of the variables.
  • Factor out the greatest common factor (GCF) of the coefficients to further simplify the expression.
  • Use a calculator to check your work and ensure that you have arrived at the correct simplified expression.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, algebraic expressions are used to describe the motion of objects, while in engineering, they are used to design and optimize systems. In economics, algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By understanding the distributive property, identifying like terms, and combining coefficients, we can simplify complex expressions and arrive at a more manageable form. We hope that this Q&A guide has provided a clear and concise overview of the process of simplifying algebraic expressions.