Simplify The Expression: \[$(x-3)(x+3)\$\]

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. One of the most common types of expressions to simplify is the product of two binomials. In this article, we will focus on simplifying the expression $(x-3)(x+3)$ using the distributive property and other algebraic techniques.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one binomial by each term in the other binomial. The distributive property can be written as:

$a(b + c) = ab + ac$

This property can be applied to both positive and negative numbers, as well as variables.

Simplifying the Expression

To simplify the expression $(x-3)(x+3)$, we can use the distributive property to expand it. We will multiply each term in the first binomial by each term in the second binomial.

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

Using the distributive property, we can simplify each term:

$x(x) = x^2$

$x(3) = 3x$

$-3(x) = -3x$

$-3(3) = -9$

Now, we can combine like terms:

$x^2 + 3x - 3x - 9$

The $3x$ and $-3x$ terms cancel each other out, leaving us with:

$x^2 - 9$

Conclusion

In this article, we simplified the expression $(x-3)(x+3)$ using the distributive property. We expanded the expression by multiplying each term in the first binomial by each term in the second binomial, and then combined like terms to simplify the expression. The final simplified expression is $x^2 - 9$.

Real-World Applications

Simplifying expressions like $(x-3)(x+3)$ has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the expression $(x-3)(x+3)$ can be used to model the motion of an object under the influence of a force. In engineering, the expression can be used to design and optimize systems such as bridges and buildings. In economics, the expression can be used to model the behavior of markets and economies.

Tips and Tricks

When simplifying expressions like $(x-3)(x+3)$, it's essential to remember the following tips and tricks:

• Use the distributive property to expand expressions.
• Combine like terms to simplify expressions.
• Check your work by plugging in values for the variable.
• Use algebraic techniques such as factoring and canceling to simplify expressions.

Common Mistakes

When simplifying expressions like $(x-3)(x+3)$, it's common to make mistakes such as:

• Forgetting to use the distributive property.
• Not combining like terms.
• Not checking your work.
• Not using algebraic techniques such as factoring and canceling.

Conclusion

In conclusion, simplifying expressions like $(x-3)(x+3)$ is a crucial skill that has many real-world applications. By using the distributive property and other algebraic techniques, we can simplify expressions and solve equations and inequalities. Remember to use the tips and tricks outlined in this article, and avoid common mistakes such as forgetting to use the distributive property and not combining like terms.

Final Answer

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Introduction

In our previous article, we simplified the expression $(x-3)(x+3)$ using the distributive property and other algebraic techniques. In this article, we will answer some common questions related to simplifying expressions like $(x-3)(x+3)$.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term in one binomial by each term in the other binomial. The distributive property can be written as:

$a(b + c) = ab + ac$

Q: How do I simplify expressions like $(x-3)(x+3)$?

A: To simplify expressions like $(x-3)(x+3)$, you can use the distributive property to expand it. Multiply each term in the first binomial by each term in the second binomial, and then combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $3x$ and $-2x$ are like terms because they both have the variable $x$ and the exponent $1$. When simplifying expressions, you can combine like terms by adding or subtracting their coefficients.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, you can plug in values for the variable and see if the expression simplifies to the correct value. For example, if you simplify the expression $(x-3)(x+3)$ to $x^2 - 9$, you can plug in $x = 4$ and see if the expression simplifies to $16 - 9 = 7$.

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

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

• Forgetting to use the distributive property.
• Not combining like terms.
• Not checking your work.
• Not using algebraic techniques such as factoring and canceling.

Q: How do I factor expressions?

A: To factor expressions, you can look for common factors in the terms. For example, if you have the expression $6x + 12$, you can factor out the common factor $6$ to get $6(x + 2)$.

Q: How do I cancel expressions?

A: To cancel expressions, you can look for common factors in the numerator and denominator. For example, if you have the expression $\frac{6x}{2x}$, you can cancel out the common factor $2x$ to get $3$.

Real-World Applications

Simplifying expressions like $(x-3)(x+3)$ has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the expression $(x-3)(x+3)$ can be used to model the motion of an object under the influence of a force. In engineering, the expression can be used to design and optimize systems such as bridges and buildings. In economics, the expression can be used to model the behavior of markets and economies.

Tips and Tricks

When simplifying expressions like $(x-3)(x+3)$, it's essential to remember the following tips and tricks:

• Use the distributive property to expand expressions.
• Combine like terms to simplify expressions.
• Check your work by plugging in values for the variable.
• Use algebraic techniques such as factoring and canceling to simplify expressions.

Conclusion

In conclusion, simplifying expressions like $(x-3)(x+3)$ is a crucial skill that has many real-world applications. By using the distributive property and other algebraic techniques, we can simplify expressions and solve equations and inequalities. Remember to use the tips and tricks outlined in this article, and avoid common mistakes such as forgetting to use the distributive property and not combining like terms.

Final Answer

The final simplified expression is $x^2 - 9$.