Simplify The Expression:${ 2y - 5(5z - 2y) - 2z }$

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, removing unnecessary parentheses, and rearranging the expression to make it easier to work with. In this article, we will simplify the given expression: $2y - 5(5z - 2y) - 2z$. We will use the order of operations (PEMDAS) and algebraic properties to simplify the expression step by step.

Understanding the Expression

The given expression is: $2y - 5(5z - 2y) - 2z$. Let's break it down and understand what it means. The expression consists of three terms:

1. $2y$
2. $-5(5z - 2y)$
3. $-2z$

The first term is a simple variable term, while the second term involves a multiplication of a constant and a binomial. The third term is another simple variable term.

Step 1: Simplify the Binomial

To simplify the expression, we need to start by simplifying the binomial inside the parentheses: $5z - 2y$. We can rewrite it as: $5z - 2y = (5z - 2y)$.

Step 2: Multiply the Constant and the Binomial

Now, we need to multiply the constant $-5$ with the binomial $(5z - 2y)$. Using the distributive property, we get: $-5(5z - 2y) = -5(5z) + -5(-2y)$.

Step 3: Simplify the Multiplication

Simplifying the multiplication, we get: $-5(5z) = -25z$ and $-5(-2y) = 10y$.

Step 4: Rewrite the Expression

Now, we can rewrite the original expression using the simplified binomial and the multiplication results: $2y - 25z + 10y - 2z$.

Step 5: Combine Like Terms

We can combine the like terms in the expression: $2y + 10y = 12y$ and $-25z - 2z = -27z$.

Step 6: Final Simplified Expression

The final simplified expression is: $12y - 27z$.

Conclusion

In this article, we simplified the given expression: $2y - 5(5z - 2y) - 2z$ using the order of operations (PEMDAS) and algebraic properties. We broke down the expression into smaller parts, simplified the binomial, multiplied the constant with the binomial, and combined like terms to get the final simplified expression: $12y - 27z$. This simplified expression is easier to work with and can be used to solve problems involving the variables $y$ and $z$.

Tips and Tricks

• When simplifying expressions, always follow the order of operations (PEMDAS).
• Use the distributive property to multiply constants with binomials.
• Combine like terms to simplify the expression.
• Check your work by plugging in values for the variables to ensure the expression is correct.

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not using the distributive property to multiply constants with binomials.
• Not combining like terms to simplify the expression.
• Not checking the work by plugging in values for the variables.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. It is used in various fields such as physics, engineering, economics, and computer science. For example, in physics, simplifying expressions is used to solve problems involving motion, energy, and momentum. In engineering, simplifying expressions is used to design and optimize systems, such as electrical circuits and mechanical systems. In economics, simplifying expressions is used to model and analyze economic systems, such as supply and demand curves. In computer science, simplifying expressions is used to optimize algorithms and data structures.

Final Thoughts

Simplifying expressions is a fundamental skill in mathematics that helps us solve problems efficiently. By following the order of operations (PEMDAS) and using algebraic properties, we can simplify complex expressions and make them easier to work with. In this article, we simplified the given expression: $2y - 5(5z - 2y) - 2z$ using the order of operations (PEMDAS) and algebraic properties. We broke down the expression into smaller parts, simplified the binomial, multiplied the constant with the binomial, and combined like terms to get the final simplified expression: $12y - 27z$. This simplified expression is easier to work with and can be used to solve problems involving the variables $y$ and $z$.

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Introduction

In our previous article, we simplified the given expression: $2y - 5(5z - 2y) - 2z$ using the order of operations (PEMDAS) and algebraic properties. We broke down the expression into smaller parts, simplified the binomial, multiplied the constant with the binomial, and combined like terms to get the final simplified expression: $12y - 27z$. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q&A

Q1: What is the order of operations (PEMDAS)?

A1: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q2: How do I simplify a binomial?

A2: To simplify a binomial, we need to follow the order of operations (PEMDAS). If the binomial is inside parentheses, we need to evaluate the expression inside the parentheses first. Then, we can simplify the binomial by combining like terms.

Q3: What is the distributive property?

A3: The distributive property is a rule that allows us to multiply a constant with a binomial. It states that:

• $a(b + c) = ab + ac$
• $a(b - c) = ab - ac$

Q4: How do I combine like terms?

A4: To combine like terms, we need to identify the terms that have the same variable and coefficient. Then, we can add or subtract the coefficients to get the final result.

Q5: What is the final simplified expression for $2y - 5(5z - 2y) - 2z$?

A5: The final simplified expression for $2y - 5(5z - 2y) - 2z$ is: $12y - 27z$.

Q6: How do I check my work?

A6: To check your work, you can plug in values for the variables and evaluate the expression. If the result is correct, then your work is correct.

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

A7: Some common mistakes to avoid when simplifying expressions include:

• Failing to follow the order of operations (PEMDAS)
• Not using the distributive property to multiply constants with binomials
• Not combining like terms to simplify the expression
• Not checking the work by plugging in values for the variables

Tips and Tricks

• Always follow the order of operations (PEMDAS) when simplifying expressions.
• Use the distributive property to multiply constants with binomials.
• Combine like terms to simplify the expression.
• Check your work by plugging in values for the variables.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. It is used in various fields such as physics, engineering, economics, and computer science. For example, in physics, simplifying expressions is used to solve problems involving motion, energy, and momentum. In engineering, simplifying expressions is used to design and optimize systems, such as electrical circuits and mechanical systems. In economics, simplifying expressions is used to model and analyze economic systems, such as supply and demand curves. In computer science, simplifying expressions is used to optimize algorithms and data structures.

Final Thoughts

Simplifying expressions is a fundamental skill in mathematics that helps us solve problems efficiently. By following the order of operations (PEMDAS) and using algebraic properties, we can simplify complex expressions and make them easier to work with. In this article, we answered some frequently asked questions (FAQs) related to simplifying expressions. We hope that this article has helped you to better understand the concept of simplifying expressions and how to apply it in real-world scenarios.