Find The Result Of: − 2 A ( 4 A + 3 B -2a(4a + 3b − 2 A ( 4 A + 3 B ]

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Introduction

In mathematics, algebraic expressions are used to represent various mathematical operations and relationships. These expressions can be simple or complex, and they often involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will focus on finding the result of a given algebraic expression, $-2a(4a + 3b)$.

Understanding the Expression

The given expression is $-2a(4a + 3b)$. To find the result of this expression, we need to understand the order of operations and how to apply the distributive property. The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This property allows us to expand the expression by multiplying each term inside the parentheses by the term outside the parentheses.

Applying the Distributive Property

To find the result of the expression $-2a(4a + 3b)$, we will apply the distributive property. We will multiply each term inside the parentheses by the term outside the parentheses, which is $-2a$. This will give us:

$-2a(4a + 3b) = -2a \cdot 4a + -2a \cdot 3b$

Simplifying the Expression

Now that we have applied the distributive property, we can simplify the expression by multiplying the terms. We will multiply $-2a$ by $4a$ and $-2a$ by $3b$:

$-2a \cdot 4a = -8a^2$

$-2a \cdot 3b = -6ab$

Combining Like Terms

Now that we have simplified the expression, we can combine like terms. We will combine the terms $-8a^2$ and $-6ab$:

$-8a^2 - 6ab$

Final Result

The final result of the expression $-2a(4a + 3b)$ is $-8a^2 - 6ab$. This is the result of applying the distributive property and simplifying the expression.

Conclusion

In this article, we have found the result of the algebraic expression $-2a(4a + 3b)$. We applied the distributive property and simplified the expression to get the final result of $-8a^2 - 6ab$. This demonstrates the importance of understanding the order of operations and applying the distributive property in algebraic expressions.

Tips and Tricks

• When working with algebraic expressions, it is essential to understand the order of operations and apply the distributive property correctly.
• To simplify an expression, multiply each term inside the parentheses by the term outside the parentheses.
• Combine like terms to get the final result.

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• Q: How do I apply the distributive property? A: To apply the distributive property, multiply each term inside the parentheses by the term outside the parentheses.
• Q: What is the final result of the expression $-2a(4a + 3b)$? A: The final result of the expression $-2a(4a + 3b)$ is $-8a^2 - 6ab$.

Related Topics

• Algebraic expressions
• Distributive property
• Order of operations
• Simplifying expressions

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton
  

Introduction

In our previous article, we discussed how to find the result of the algebraic expression $-2a(4a + 3b)$. We applied the distributive property and simplified the expression to get the final result of $-8a^2 - 6ab$. In this article, we will answer some frequently asked questions about algebraic expressions and the distributive property.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means that we can multiply each term inside the parentheses by the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, follow these steps:

1. Identify the term outside the parentheses.
2. Multiply each term inside the parentheses by the term outside the parentheses.
3. Simplify the expression by combining like terms.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property and the commutative property are two different mathematical concepts. The distributive property states that we can multiply each term inside the parentheses by the term outside the parentheses, while the commutative property states that the order of the terms does not change the result.

Q: Can I apply the distributive property to expressions with more than two terms inside the parentheses?

A: Yes, you can apply the distributive property to expressions with more than two terms inside the parentheses. For example, if you have the expression $a(2b + 3c + 4d)$, you can multiply each term inside the parentheses by $a$.

Q: How do I simplify an expression after applying the distributive property?

A: To simplify an expression after applying the distributive property, follow these steps:

1. Multiply each term inside the parentheses by the term outside the parentheses.
2. Combine like terms to get the final result.

Q: What is the final result of the expression $-2a(4a + 3b)$?

A: The final result of the expression $-2a(4a + 3b)$ is $-8a^2 - 6ab$.

Q: Can I apply the distributive property to expressions with variables and constants?

A: Yes, you can apply the distributive property to expressions with variables and constants. For example, if you have the expression $a(2b + 3c + 4d)$, you can multiply each term inside the parentheses by $a$.

Q: How do I know when to apply the distributive property?

A: You should apply the distributive property when you have an expression with parentheses and you need to multiply each term inside the parentheses by the term outside the parentheses.

Conclusion

In this article, we have answered some frequently asked questions about algebraic expressions and the distributive property. We have discussed how to apply the distributive property, how to simplify expressions, and how to identify the final result of an expression. We hope that this article has been helpful in clarifying any confusion you may have had about algebraic expressions and the distributive property.

Tips and Tricks

• Always apply the distributive property when you have an expression with parentheses.
• Simplify expressions by combining like terms.
• Use the distributive property to expand expressions with variables and constants.

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• Q: How do I apply the distributive property? A: To apply the distributive property, follow these steps: 1. Identify the term outside the parentheses. 2. Multiply each term inside the parentheses by the term outside the parentheses. 3. Simplify the expression by combining like terms.
• Q: What is the final result of the expression $-2a(4a + 3b)$? A: The final result of the expression $-2a(4a + 3b)$ is $-8a^2 - 6ab$.

Related Topics

• Algebraic expressions
• Distributive property
• Order of operations
• Simplifying expressions

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton