Simplify The Expression: { (x+3)(x-3)(3x+2)$}$

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Introduction

In this article, we will simplify the given expression $(x+3)(x-3)(3x+2)$. This involves expanding the product of three binomials and combining like terms to obtain the simplified form of the expression. We will use the distributive property and the commutative property of multiplication to simplify the expression.

Understanding the Expression

The given expression is a product of three binomials: $(x+3)$, $(x-3)$, and $(3x+2)$. To simplify this expression, we need to multiply these three binomials together. We can start by multiplying the first two binomials, $(x+3)$ and $(x-3)$, and then multiply the result by the third binomial, $(3x+2)$.

Expanding the Product

To expand the product of the three binomials, we can use the distributive property. This property states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. We can apply this property to each term in the product.

First, we multiply the first two binomials, $(x+3)$ and $(x-3)$:

$$(x+3)(x-3) = x(x-3) + 3(x-3)$$

Using the distributive property, we can expand this expression as:

$$x(x-3) + 3(x-3) = x^2 - 3x + 3x - 9$$

Combining like terms, we get:

$$x^2 - 9$$

Now, we multiply this result by the third binomial, $(3x+2)$:

$$(x^2 - 9)(3x+2) = x^2(3x+2) - 9(3x+2)$$

Using the distributive property again, we can expand this expression as:

$$x^2(3x+2) - 9(3x+2) = 3x^3 + 2x^2 - 27x - 18$$

Simplifying the Expression

The expression $3x^3 + 2x^2 - 27x - 18$ is the simplified form of the original expression $(x+3)(x-3)(3x+2)$. This expression cannot be simplified further using basic algebraic manipulations.

Conclusion

In this article, we simplified the given expression $(x+3)(x-3)(3x+2)$ by expanding the product of three binomials and combining like terms. We used the distributive property and the commutative property of multiplication to simplify the expression. The simplified form of the expression is $3x^3 + 2x^2 - 27x - 18$.

Example Use Cases

The expression $(x+3)(x-3)(3x+2)$ can be used in various mathematical contexts, such as:

• Algebra: The expression can be used to demonstrate the distributive property and the commutative property of multiplication.
• Calculus: The expression can be used to find the derivative of a function.
• Physics: The expression can be used to model the motion of an object.

Tips and Tricks

When simplifying expressions, it is essential to use the distributive property and the commutative property of multiplication. These properties can help to simplify complex expressions and make them easier to work with.

Frequently Asked Questions

• Q: What is the simplified form of the expression $(x+3)(x-3)(3x+2)$?
• A: The simplified form of the expression is $3x^3 + 2x^2 - 27x - 18$.
• Q: How do I simplify the expression $(x+3)(x-3)(3x+2)$?
• A: To simplify the expression, you can use the distributive property and the commutative property of multiplication to expand the product of the three binomials and combine like terms.

Further Reading

For more information on simplifying expressions, you can refer to the following resources:

• Algebra textbooks: Many algebra textbooks provide examples and exercises on simplifying expressions.
• Online resources: Websites such as Khan Academy and Mathway provide video lessons and interactive exercises on simplifying expressions.
• Calculus textbooks: Calculus textbooks often provide examples and exercises on finding the derivative of a function, which can involve simplifying expressions.

Conclusion

In this article, we simplified the given expression $(x+3)(x-3)(3x+2)$ by expanding the product of three binomials and combining like terms. We used the distributive property and the commutative property of multiplication to simplify the expression. The simplified form of the expression is $3x^3 + 2x^2 - 27x - 18$. We also provided example use cases, tips and tricks, and frequently asked questions to help readers understand the concept better.

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Introduction

In our previous article, we simplified the given expression $(x+3)(x-3)(3x+2)$ by expanding the product of three binomials and combining like terms. We used the distributive property and the commutative property of multiplication to simplify the expression. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What is the simplified form of the expression $(x+3)(x-3)(3x+2)$?

A: The simplified form of the expression is $3x^3 + 2x^2 - 27x - 18$.

Q: How do I simplify the expression $(x+3)(x-3)(3x+2)$?

A: To simplify the expression, you can use the distributive property and the commutative property of multiplication to expand the product of the three binomials and combine like terms.

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 can be used to expand the product of two or more binomials.

Q: What is the commutative property of multiplication?

A: The commutative property of multiplication is a mathematical property that states that for any real numbers $a$ and $b$, $ab = ba$. This property can be used to rearrange the terms in an expression without changing its value.

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

A: To use the distributive property to simplify an expression, you can multiply each term in one binomial by each term in the other binomial. For example, to simplify the expression $(x+3)(x-3)$, you can multiply each term in the first binomial by each term in the second binomial:

$$(x+3)(x-3) = x(x-3) + 3(x-3)$$

Q: How do I use the commutative property of multiplication to simplify an expression?

A: To use the commutative property of multiplication to simplify an expression, you can rearrange the terms in the expression without changing its value. For example, to simplify the expression $(x+3)(x-3)$, you can rearrange the terms as follows:

$$(x+3)(x-3) = (x-3)(x+3)$$

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

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

• Not using the distributive property to expand the product of two or more binomials
• Not combining like terms
• Not using the commutative property of multiplication to rearrange the terms in an expression
• Not checking the expression for errors

Q: How do I check an expression for errors?

A: To check an expression for errors, you can use the following steps:

• Simplify the expression using the distributive property and the commutative property of multiplication
• Combine like terms
• Check the expression for any errors or inconsistencies
• Verify the expression using a calculator or other mathematical tool

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions. We provided examples and explanations to help readers understand the concept better. We also provided tips and tricks to help readers avoid common mistakes when simplifying expressions.

Example Use Cases

The expression $(x+3)(x-3)(3x+2)$ can be used in various mathematical contexts, such as:

• Algebra: The expression can be used to demonstrate the distributive property and the commutative property of multiplication.
• Calculus: The expression can be used to find the derivative of a function.
• Physics: The expression can be used to model the motion of an object.

Tips and Tricks

When simplifying expressions, it is essential to use the distributive property and the commutative property of multiplication. These properties can help to simplify complex expressions and make them easier to work with.

Frequently Asked Questions

• Q: What is the simplified form of the expression $(x+3)(x-3)(3x+2)$?
• A: The simplified form of the expression is $3x^3 + 2x^2 - 27x - 18$.
• Q: How do I simplify the expression $(x+3)(x-3)(3x+2)$?
• A: To simplify the expression, you can use the distributive property and the commutative property of multiplication to expand the product of the three binomials and combine like terms.

Further Reading

For more information on simplifying expressions, you can refer to the following resources:

• Algebra textbooks: Many algebra textbooks provide examples and exercises on simplifying expressions.
• Online resources: Websites such as Khan Academy and Mathway provide video lessons and interactive exercises on simplifying expressions.
• Calculus textbooks: Calculus textbooks often provide examples and exercises on finding the derivative of a function, which can involve simplifying expressions.

Conclusion

In this article, we provided a Q&A section to help readers understand the concept of simplifying expressions better. We answered some frequently asked questions and provided examples and explanations to help readers understand the concept better. We also provided tips and tricks to help readers avoid common mistakes when simplifying expressions.