Expand The Expression: $ (x-5)(x+3) $

Mar 13, 2025 by ADMIN 38 views

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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 $(x-5)(x+3)$ using the distributive property.

The Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying the terms inside the parentheses. The distributive property states that for any real numbers $a$ , $b$ , and $c$ , the following equation holds:

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

This property can be applied to any expression with two or more terms inside the parentheses.

Expanding the Expression

To expand the expression $(x-5)(x+3)$ , we will use the distributive property. We will multiply each term inside the first parentheses by each term inside the second parentheses.

$(x-5)(x+3) = x(x+3) - 5(x+3)$

Applying the Distributive Property

Now, we will apply the distributive property to each term inside the parentheses.

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

$-5(x+3) = -5x - 15$

Combining Like Terms

Now that we have expanded the expression, we can combine like terms to simplify it.

$x^2 + 3x - 5x - 15 = x^2 - 2x - 15$

Conclusion

In this article, we learned how to expand the expression $(x-5)(x+3)$ using the distributive property. We applied the distributive property to each term inside the parentheses and combined like terms to simplify the expression. This skill is essential in algebra and is used to solve equations and simplify expressions.

Examples

Here are some examples of expanding expressions using the distributive property:

$(x+2)(x-4) = x^2 - 2x - 8$
$(x-3)(x+2) = x^2 - x - 6$
$(x+5)(x-1) = x^2 + 4x - 5$

Tips and Tricks

Here are some tips and tricks to help you expand expressions using the distributive property:

Make sure to apply the distributive property to each term inside the parentheses.
Combine like terms to simplify the expression.
Use the distributive property to expand expressions with two or more terms inside the parentheses.
Practice, practice, practice! The more you practice, the more comfortable you will become with expanding expressions using the distributive property.

Real-World Applications

Expanding expressions using the distributive property has many real-world applications. Here are a few examples:

In physics, expanding expressions is used to describe the motion of objects.
In engineering, expanding expressions is used to design and build structures.
In economics, expanding expressions is used to model and analyze economic systems.

Final Thoughts

In conclusion, expanding expressions using the distributive property is a crucial skill in algebra. By applying the distributive property to each term inside the parentheses and combining like terms, we can simplify expressions and solve equations. With practice and patience, you will become proficient in expanding expressions using the distributive property and be able to apply it to real-world problems.

Additional Resources

If you want to learn more about expanding expressions using the distributive property, here are some additional resources:

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

Frequently Asked Questions

Here are some frequently asked questions about expanding expressions using the distributive property:

Q: What is the distributive property? A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying the terms inside the parentheses.
Q: How do I apply the distributive property? A: To apply the distributive property, multiply each term inside the first parentheses by each term inside the second parentheses.
Q: What are like terms? A: Like terms are terms that have the same variable and exponent.

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Introduction

In our previous article, we learned how to expand expressions using the distributive property. However, we know that there are many more questions and concerns that you may have. In this article, we will address some of the most frequently asked questions about expanding expressions using the distributive property.

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 the terms inside the parentheses. It states that for any real numbers $a$ , $b$ , and $c$ , the following equation holds:

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

Q: How do I apply the distributive property?

A: To apply the distributive property, multiply each term inside the first parentheses by each term inside the second parentheses. For example, to expand the expression $(x-5)(x+3)$ , we would multiply each term inside the first parentheses by each term inside the second parentheses:

$(x-5)(x+3) = x(x+3) - 5(x+3)$

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ and the exponent $1$ . On the other hand, $2x$ and $3y$ are not like terms because they have different variables.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, to combine the like terms $2x$ and $5x$ , we would add their coefficients:

$2x + 5x = 7x$

Q: What is the difference between expanding and simplifying an expression?

A: Expanding an expression involves multiplying the terms inside the parentheses to get a single expression. Simplifying an expression involves combining like terms to get a simpler expression.

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

A: Yes, you can use the distributive property to expand expressions with more than two terms inside the parentheses. For example, to expand the expression $(x-5)(x+3)(x-2)$ , we would multiply each term inside the first parentheses by each term inside the second parentheses, and then multiply the result by each term inside the third parentheses.

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

A: You should use the distributive property whenever you need to expand an expression with two or more terms inside the parentheses. This is a fundamental concept in algebra, and it is used to solve equations and simplify expressions.