Simplify The Expression:${ 1.2 \frac{3}{5} V^2 (3v^2 - 9) }$

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the underlying concepts. In this article, we will focus on simplifying the given expression, which involves multiplying and combining like terms. We will break down the expression step by step, using various mathematical techniques to simplify it.

Understanding the Expression

The given expression is $1.2 \frac{3}{5} v^2 (3v^2 - 9)$. This expression involves several components, including a fraction, a variable raised to a power, and a polynomial expression. To simplify this expression, we need to understand the rules of algebra and how to manipulate expressions using various mathematical operations.

Distributive Property

The distributive property is a fundamental concept in algebra that allows us to multiply a single term by multiple terms. In this case, we can use the distributive property to expand the expression $(3v^2 - 9)$.

(3v^2 - 9) = 3v^2 - 9

Multiplying the Terms

Now that we have expanded the expression, we can multiply the terms together. We will start by multiplying the fraction $\frac{3}{5}$ by the variable $v^2$.

1.2 \frac{3}{5} v^2 = \frac{1.2 \times 3}{5} v^2

Simplifying the Fraction

We can simplify the fraction by multiplying the numerator and denominator.

\frac{1.2 \times 3}{5} = \frac{3.6}{5}

Multiplying the Terms Together

Now that we have simplified the fraction, we can multiply the terms together.

\frac{3.6}{5} v^2 (3v^2 - 9) = \frac{3.6}{5} v^2 (3v^2) - \frac{3.6}{5} v^2 (9)

Combining Like Terms

We can combine like terms by adding or subtracting the coefficients of the same variables.

\frac{3.6}{5} v^2 (3v^2) - \frac{3.6}{5} v^2 (9) = \frac{3.6}{5} v^4 - \frac{3.6}{5} v^2 (9)

Simplifying the Expression

We can simplify the expression by multiplying the terms together.

\frac{3.6}{5} v^4 - \frac{3.6}{5} v^2 (9) = \frac{3.6}{5} v^4 - \frac{32.4}{5} v^2

Final Answer

The final answer is $\boxed{\frac{3.6}{5} v^4 - \frac{32.4}{5} v^2}$.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the underlying concepts. In this article, we have focused on simplifying the given expression, which involves multiplying and combining like terms. We have used various mathematical techniques, including the distributive property and combining like terms, to simplify the expression. The final answer is $\frac{3.6}{5} v^4 - \frac{32.4}{5} v^2$.

Tips and Tricks

• When simplifying algebraic expressions, it is essential to understand the rules of algebra and how to manipulate expressions using various mathematical operations.
• The distributive property is a fundamental concept in algebra that allows us to multiply a single term by multiple terms.
• Combining like terms is a crucial step in simplifying algebraic expressions.
• When multiplying terms together, it is essential to follow the order of operations (PEMDAS).

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a fundamental concept in algebra that allows us to multiply a single term by multiple terms.
• Q: How do I combine like terms? A: To combine like terms, you need to add or subtract the coefficients of the same variables.
• Q: What is the final answer? A: The final answer is $\boxed{\frac{3.6}{5} v^4 - \frac{32.4}{5} v^2}$.

References

• [1] Algebra: A Comprehensive Introduction, by Gary Rockswold
• [2] Calculus: Early Transcendentals, by James Stewart
• [3] Mathematics for Computer Science, by Eric Lehman, F Thomson Leighton, and Albert R Meyer

Further Reading

• Simplifying Algebraic Expressions: A Step-by-Step Guide
• Algebraic Manipulation: A Comprehensive Guide
• Mathematics for Computer Science: A Comprehensive Introduction
  

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Introduction

In our previous article, we simplified the expression $1.2 \frac{3}{5} v^2 (3v^2 - 9)$ using various mathematical techniques. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to multiply a single term by multiple terms. It states that for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the same variables. For example, if you have the expression 2x + 3x, you can combine the like terms by adding the coefficients:

2x + 3x = 5x

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 we have multiple operations in 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 fractions?

A: To simplify an expression with fractions, you need to follow these steps:

1. Multiply the numerator and denominator of each fraction by the least common multiple (LCM) of the denominators.
2. Simplify the resulting expression by canceling out any common factors between the numerator and denominator.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same. For example, in the expression 2x, x is a variable because its value can change, while 2 is a constant because its value remains the same.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to follow these steps:

1. Evaluate any exponential expressions by raising the base to the power of the exponent.
2. Simplify the resulting expression by combining like terms.

Q: What is the final answer to the expression $1.2 \frac{3}{5} v^2 (3v^2 - 9)$?

A: The final answer to the expression $1.2 \frac{3}{5} v^2 (3v^2 - 9)$ is $\boxed{\frac{3.6}{5} v^4 - \frac{32.4}{5} v^2}$.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics, and it requires a deep understanding of the underlying concepts. In this article, we have answered some frequently asked questions related to simplifying algebraic expressions. We hope that this article has been helpful in clarifying any doubts you may have had.

Tips and Tricks

• When simplifying algebraic expressions, it is essential to understand the rules of algebra and how to manipulate expressions using various mathematical operations.
• The distributive property is a fundamental concept in algebra that allows us to multiply a single term by multiple terms.
• Combining like terms is a crucial step in simplifying algebraic expressions.
• When multiplying terms together, it is essential to follow the order of operations (PEMDAS).

Frequently Asked Questions

• Q: What is the distributive property? A: The distributive property is a fundamental concept in algebra that allows us to multiply a single term by multiple terms.
• Q: How do I combine like terms? A: To combine like terms, you need to add or subtract the coefficients of the same variables.
• Q: What is the final answer to the expression $1.2 \frac{3}{5} v^2 (3v^2 - 9)$? A: The final answer to the expression $1.2 \frac{3}{5} v^2 (3v^2 - 9)$ is $\boxed{\frac{3.6}{5} v^4 - \frac{32.4}{5} v^2}$.

References

• [1] Algebra: A Comprehensive Introduction, by Gary Rockswold
• [2] Calculus: Early Transcendentals, by James Stewart
• [3] Mathematics for Computer Science, by Eric Lehman, F Thomson Leighton, and Albert R Meyer

Further Reading

• Simplifying Algebraic Expressions: A Step-by-Step Guide
• Algebraic Manipulation: A Comprehensive Guide
• Mathematics for Computer Science: A Comprehensive Introduction