Simplify The Expression: ${ Y^2(-4y + 5) - 6y^2 }$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. In this article, we will focus on simplifying the given expression: $y^2(-4y + 5) - 6y^2$. We will break down the process into manageable steps, making it easy to understand and follow.

Understanding the Expression

Before we start simplifying the expression, let's break it down and understand its components. The given expression is a combination of two terms:

1. $y^2(-4y + 5)$
2. $-6y^2$

The first term is a product of two expressions: $y^2$ and $(-4y + 5)$. The second term is a simple expression: $-6y^2$.

Step 1: Distribute the Negative Sign

To simplify the expression, we need to start by distributing the negative sign to the second term. When we distribute the negative sign, it changes the sign of the term. So, $-6y^2$ becomes $-6y^2$ (no change).

y^2(-4y + 5) - 6y^2 = y^2(-4y + 5) + 6y^2

Step 2: Distribute $y^2$ to the Terms Inside the Parentheses

Now, we need to distribute $y^2$ to the terms inside the parentheses: $-4y + 5$. When we distribute $y^2$, we multiply it by each term inside the parentheses.

y^2(-4y + 5) + 6y^2 = -4y^3 + 5y^2 + 6y^2

Step 3: Combine Like Terms

Now that we have distributed $y^2$ to the terms inside the parentheses, we can combine like terms. In this case, we have two terms with the same variable: $5y^2$ and $6y^2$. We can combine these terms by adding their coefficients.

-4y^3 + 5y^2 + 6y^2 = -4y^3 + 11y^2

Conclusion

In this article, we simplified the given expression: $y^2(-4y + 5) - 6y^2$. We broke down the process into manageable steps, making it easy to understand and follow. By distributing the negative sign, distributing $y^2$ to the terms inside the parentheses, and combining like terms, we arrived at the simplified expression: $-4y^3 + 11y^2$.

Tips and Tricks

• When simplifying expressions, always start by distributing the negative sign to the terms inside the parentheses.
• When distributing a variable to the terms inside the parentheses, multiply it by each term.
• When combining like terms, add the coefficients of the terms with the same variable.

Common Mistakes to Avoid

• Not distributing the negative sign to the terms inside the parentheses.
• Not multiplying the variable by each term inside the parentheses.
• Not combining like terms.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics, and it has many real-world applications. For example, in physics, we use simplifying expressions to solve problems involving motion and energy. In engineering, we use simplifying expressions to design and optimize systems.

Final Thoughts

Introduction

In our previous article, we simplified the expression: $y^2(-4y + 5) - 6y^2$. We broke down the process into manageable steps, making it easy to understand and follow. In this article, we will answer some frequently asked questions about simplifying expressions.

Q: What is the first step in simplifying an expression?

A: The first step in simplifying an expression is to distribute the negative sign to the terms inside the parentheses. This will change the sign of the terms inside the parentheses.

Q: How do I distribute a variable to the terms inside the parentheses?

A: To distribute a variable to the terms inside the parentheses, you multiply it by each term. For example, if you have the expression $y^2(-4y + 5)$, you would multiply $y^2$ by $-4y$ and $y^2$ by $5$.

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

A: Combining like terms is a step in simplifying an expression. When you combine like terms, you add the coefficients of the terms with the same variable. Simplifying an expression is the process of reducing it to its simplest form by combining like terms, distributing variables, and eliminating parentheses.

Q: How do I know if I have simplified an expression correctly?

A: To check if you have simplified an expression correctly, you can plug in a value for the variable and see if the expression evaluates to the correct value. You can also use a calculator or a computer program to check your work.

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

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

• Not distributing the negative sign to the terms inside the parentheses.
• Not multiplying the variable by each term inside the parentheses.
• Not combining like terms.
• Not eliminating parentheses.

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through problems in a textbook or online resource. You can also try simplifying expressions on your own by creating your own problems and solutions.

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

A: Simplifying expressions has many real-world applications, including:

• Physics: Simplifying expressions is used to solve problems involving motion and energy.
• Engineering: Simplifying expressions is used to design and optimize systems.
• Computer Science: Simplifying expressions is used in algorithms and data structures.

Q: Can I use a calculator or computer program to simplify expressions?

A: Yes, you can use a calculator or computer program to simplify expressions. However, it's still important to understand the process of simplifying expressions by hand, as this will help you to identify and correct errors.

Conclusion

Simplifying expressions is a fundamental concept in mathematics, and it requires practice and patience to master. By following the steps outlined in this article, you can simplify expressions with ease and accuracy. Remember to distribute the negative sign, distribute the variable to the terms inside the parentheses, and combine like terms. With practice and patience, you will become proficient in simplifying expressions and solving problems in mathematics.

Tips and Tricks

• Always start by distributing the negative sign to the terms inside the parentheses.
• When distributing a variable to the terms inside the parentheses, multiply it by each term.
• When combining like terms, add the coefficients of the terms with the same variable.
• Use a calculator or computer program to check your work and identify errors.

Common Mistakes to Avoid

• Not distributing the negative sign to the terms inside the parentheses.
• Not multiplying the variable by each term inside the parentheses.
• Not combining like terms.
• Not eliminating parentheses.

Real-World Applications

Simplifying expressions has many real-world applications, including physics, engineering, and computer science. By understanding and mastering the process of simplifying expressions, you can solve problems and make informed decisions in a variety of fields.