What Is The Simplest Form Of This Expression?$-2b(-5b + 4) - 4b^2$Enter The Correct Answer.

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 explore the process of simplifying algebraic expressions, focusing on the simplest form of the given expression: $-2b(-5b + 4) - 4b^2$. We will break down the expression into manageable parts, apply the rules of algebra, and arrive at the final simplified form.

Understanding the Expression

Before we dive into simplifying the expression, let's take a closer look at what we're dealing with. The given expression is:

$$-2b(-5b + 4) - 4b^2$$

This expression consists of two main parts:

1. Distributive Property: The first part, $-2b(-5b + 4)$, involves the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
2. Simplifying the Second Part: The second part, $-4b^2$, is a simple quadratic expression that can be simplified using the rules of algebra.

Step 1: Apply the Distributive Property

To simplify the first part of the expression, we need to apply the distributive property. This means that we need to multiply the term $-2b$ by each term inside the parentheses, $-5b$ and $4$.

$$-2b(-5b + 4) = -2b(-5b) + (-2b)(4)$$

Using the distributive property, we can rewrite the expression as:

$$25b^2 - 8b$$

Step 2: Simplify the Second Part

The second part of the expression, $-4b^2$, is a simple quadratic expression that can be simplified using the rules of algebra. Since there are no like terms to combine, we can leave the expression as is.

Step 3: Combine Like Terms

Now that we have simplified both parts of the expression, we can combine like terms to arrive at the final simplified form.

$$25b^2 - 8b - 4b^2$$

Using the commutative property of addition, we can rearrange the terms to get:

$$25b^2 - 4b^2 - 8b$$

Now, we can combine the like terms:

$$21b^2 - 8b$$

Conclusion

In this article, we have simplified the given expression $-2b(-5b + 4) - 4b^2$ using the rules of algebra. We applied the distributive property to simplify the first part of the expression and combined like terms to arrive at the final simplified form: $21b^2 - 8b$. This simplified expression is the simplest form of the given expression.

Final Answer

Introduction

In our previous article, we explored the process of simplifying algebraic expressions, focusing on the simplest form of the given expression: $-2b(-5b + 4) - 4b^2$. We broke down the expression into manageable parts, applied the rules of algebra, and arrived at the final simplified form: $21b^2 - 8b$. In this article, we will answer some frequently asked questions about 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 $c$, $a(b + c) = ab + ac$. This property is used to simplify expressions by multiplying each term inside the parentheses by the term outside the parentheses.

Q: How do I apply the distributive property to simplify an expression?

A: To apply the distributive property, you need to multiply the term outside the parentheses by each term inside the parentheses. For example, if you have the expression $-2b(-5b + 4)$, you would multiply $-2b$ by $-5b$ and $4$ separately to get $25b^2 - 8b$.

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

A: Combining like terms involves adding or subtracting terms that have the same variable and exponent. Simplifying an expression, on the other hand, involves applying the rules of algebra to rewrite the expression in a simpler form. While combining like terms is an important step in simplifying an expression, it is not the same thing.

Q: How do I know when to combine like terms and when to simplify an expression?

A: You should combine like terms when you have two or more terms that have the same variable and exponent. You should simplify an expression when you have an expression that can be rewritten in a simpler form using the rules of algebra.

Q: Can I simplify an expression by rearranging the terms?

A: Yes, you can simplify an expression by rearranging the terms. However, this is not the same as simplifying an expression using the rules of algebra. Rearranging the terms can make the expression easier to read, but it does not necessarily simplify the expression.

Q: How do I know if an expression is in its simplest form?

A: An expression is in its simplest form when it cannot be rewritten in a simpler form using the rules of algebra. This means that there are no like terms to combine, and the expression cannot be simplified further.

Q: Can I use a calculator to simplify an expression?

A: Yes, you can use a calculator to simplify an expression. However, it is always a good idea to check your work by hand to make sure that the calculator is giving you the correct answer.

Conclusion

In this article, we have answered some frequently asked questions about simplifying algebraic expressions. We have discussed the distributive property, combining like terms, and simplifying expressions using the rules of algebra. By following these tips and techniques, you can simplify algebraic expressions with confidence.

Final Tips

• Always read the expression carefully before simplifying it.
• Use the distributive property to simplify expressions with parentheses.
• Combine like terms to simplify expressions with multiple terms.
• Check your work by hand to make sure that the calculator is giving you the correct answer.
• Practice, practice, practice! The more you practice simplifying algebraic expressions, the more comfortable you will become with the process.