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

Mar 11, 2025 by ADMIN 39 views

$Expand the Expression: ${$(x-3)(x+3)\$}$$

Introduction

In algebra, expanding expressions is a crucial skill that helps us simplify and solve equations. When we expand an expression, we multiply the terms inside the parentheses to get a single expression. In this article, we will learn how to expand the expression ${$ (x-3)(x+3)$}$. We will use the distributive property to multiply the terms and simplify the expression.

Understanding the Distributive Property

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 numbers a, b, and c:

a(b + c) = ab + ac

This property can be extended to more than two terms, and it is the key to expanding expressions.

Expanding the Expression

To expand the expression ${$ (x-3)(x+3)$}$, we will use the distributive property. We will multiply the first term, x, by both terms inside the second parentheses, x and 3. Then, we will multiply the second term, -3, by both terms inside the second parentheses, x and 3.

Step 1: Multiply x by x and 3

We will start by multiplying x by x and 3:

x(x) = x^2 x(3) = 3x

Step 2: Multiply -3 by x and 3

Next, we will multiply -3 by x and 3:

-3(x) = -3x -3(3) = -9

Step 3: Combine the Terms

Now, we will combine the terms we have multiplied:

x^2 + 3x - 3x - 9

Step 4: Simplify the Expression

Finally, we will simplify the expression by combining like terms:

x^2 - 9

Conclusion

In this article, we learned how to expand the expression ${$ (x-3)(x+3)$}$ using the distributive property. We multiplied the terms inside the parentheses and simplified the expression to get the final result, x^2 - 9. This is an important skill in algebra that helps us solve equations and simplify expressions.

Tips and Tricks

When expanding expressions, always use the distributive property to multiply the terms.
Make sure to combine like terms to simplify the expression.
Practice expanding expressions with different variables and coefficients to become more comfortable with the process.

Common Mistakes

Failing to use the distributive property when expanding expressions.
Not combining like terms to simplify the expression.
Making errors when multiplying terms.

Real-World Applications

Expanding expressions is a crucial skill in many real-world applications, including:

Physics: Expanding expressions is used to describe the motion of objects and the forces acting on them.
Engineering: Expanding expressions is used to design and analyze complex systems.
Computer Science: Expanding expressions is used in algorithms and data structures.

Final Thoughts

Expanding expressions is a fundamental skill in algebra that helps us simplify and solve equations. By using the distributive property and combining like terms, we can expand expressions and get the final result. With practice and patience, anyone can become proficient in expanding expressions and apply it to real-world problems.

Additional Resources

For more information on expanding expressions, check out the following resources:

Khan Academy: Expanding Expressions
Mathway: Expanding Expressions
Wolfram Alpha: Expanding Expressions

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 expand an expression? A: To expand an expression, use the distributive property to multiply the terms inside the parentheses and combine like terms to simplify the expression.

Q: What are some common mistakes when expanding expressions? A: Failing to use the distributive property, not combining like terms, and making errors when multiplying terms are some common mistakes when expanding expressions.

Introduction

Expanding expressions is a fundamental skill in algebra that helps us simplify and solve equations. In our previous article, we learned how to expand the expression ${$ (x-3)(x+3)$}$ using the distributive property. In this article, we will answer some frequently asked questions about expanding 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 numbers a, b, and c:

a(b + c) = ab + ac

This property can be extended to more than two terms, and it is the key to expanding expressions.

Q: How do I expand an expression?

A: To expand an expression, use the distributive property to multiply the terms inside the parentheses and combine like terms to simplify the expression. Here's a step-by-step guide:

Multiply the first term by both terms inside the second parentheses.
Multiply the second term by both terms inside the second parentheses.
Combine the terms you have multiplied.
Simplify the expression by combining like terms.

Q: What are some common mistakes when expanding expressions?

A: Failing to use the distributive property, not combining like terms, and making errors when multiplying terms are some common mistakes when expanding expressions.

Q: How do I know if I have expanded an expression correctly?

A: To check if you have expanded an expression correctly, follow these steps:

Multiply the terms inside the parentheses using the distributive property.
Combine like terms to simplify the expression.
Check if the expression is in its simplest form.

Q: Can I use the distributive property to expand expressions with more than two terms?

A: Yes, you can use the distributive property to expand expressions with more than two terms. For example, to expand the expression ${$ (x-3)(x+3)(x-2)$}$, you would multiply the first two terms using the distributive property, and then multiply the result by the third term.

Q: How do I expand expressions with variables and coefficients?

A: To expand expressions with variables and coefficients, use the distributive property to multiply the terms inside the parentheses. For example, to expand the expression ${$ (2x-3)(x+2)$}$, you would multiply the first term by both terms inside the second parentheses, and then multiply the second term by both terms inside the second parentheses.

Q: Can I use the distributive property to expand expressions with negative numbers?

A: Yes, you can use the distributive property to expand expressions with negative numbers. For example, to expand the expression ${$ (-x+3)(x-2)$}$, you would multiply the first term by both terms inside the second parentheses, and then multiply the second term by both terms inside the second parentheses.

Q: How do I simplify expressions after expanding them?

A: To simplify expressions after expanding them, combine like terms to get the final result. For example, if you have expanded the expression ${$ (x-3)(x+3)$}$ to get ${$ x^2-9$}$, you would simplify the expression by combining the like terms.