Simplify The Expression: \[$-5r(-4r - 2)\$\]

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Introduction

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In this article, we will simplify the given expression $-5r(-4r - 2)$. This involves using the distributive property and simplifying the resulting expression. We will also provide step-by-step solutions to help readers understand the process.

Understanding the Expression

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The given expression is $-5r(-4r - 2)$. This expression involves two variables, $r$ and $-4r - 2$. To simplify this expression, we need to use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Step 1: Apply the Distributive Property

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To simplify the expression, we will apply the distributive property. We will multiply the term $-5r$ with the term $(-4r - 2)$.

-5r(-4r - 2) = -5r(-4r) - 5r(-2)

Step 2: Simplify the Expression

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Now, we will simplify the expression by multiplying the terms.

-5r(-4r) = 20r^2
-5r(-2) = 10r

Step 3: Combine Like Terms

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We will now combine the like terms in the expression.

20r^2 + 10r

Conclusion

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In this article, we simplified the expression $-5r(-4r - 2)$ using the distributive property and combining like terms. The simplified expression is $20r^2 + 10r$. We hope this article has provided readers with a clear understanding of how to simplify expressions involving variables.

Frequently Asked Questions

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Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Q: How do I simplify an expression involving variables?

A: To simplify an expression involving variables, you can use the distributive property and combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power.

Final Answer

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The final answer is: $\boxed{20r^2 + 10r}$

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Introduction

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In our previous article, we simplified the expression $-5r(-4r - 2)$ using the distributive property and combining like terms. In this article, we will provide a Q&A section to help readers understand the process and address any questions they may have.

Q&A

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Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property allows us to multiply a single term by two or more terms inside parentheses.

Q: How do I simplify an expression involving variables?

A: To simplify an expression involving variables, you can use the distributive property and combine like terms. Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you can add or subtract the coefficients of the like terms. For example, if you have the expression $2x + 5x$, you can combine the like terms by adding the coefficients: $2x + 5x = 7x$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The order of operations is:

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

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, you can use the distributive property and combine like terms. For example, if you have the expression $2x + 3y + 4x$, you can combine the like terms by adding the coefficients: $2x + 3y + 4x = 6x + 3y$.

Example Problems

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Problem 1: Simplify the expression $-3x(-2x + 5)$

A: To simplify this expression, we can use the distributive property and combine like terms.

-3x(-2x + 5) = -3x(-2x) + -3x(5)
= 6x^2 - 15x

Problem 2: Simplify the expression $2x + 4y - 3x$

A: To simplify this expression, we can combine like terms.

2x + 4y - 3x = -x + 4y

Conclusion

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In this article, we provided a Q&A section to help readers understand the process of simplifying expressions involving variables. We also provided example problems to help readers practice simplifying expressions. We hope this article has provided readers with a clear understanding of how to simplify expressions involving variables.

Final Answer

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The final answer is: $\boxed{20r^2 + 10r}$