Expand And Simplify: { (a - 4)(a + 8)$}$

Mar 13, 2025 by ADMIN 41 views

**Expanding and Simplifying Algebraic Expressions: A Step-by-Step Guide**

Introduction

Algebraic expressions are a fundamental concept in mathematics, and expanding and simplifying them is a crucial skill for students to master. In this article, we will focus on expanding and simplifying the given expression: $(a - 4)(a + 8)$ . We will break down the process into manageable steps, making it easier for readers to understand and apply the concepts.

What is Expanding and Simplifying Algebraic Expressions?

Expanding and simplifying algebraic expressions involves using mathematical operations to rewrite an expression in a simpler form. This process can involve multiplying, adding, and subtracting terms, as well as combining like terms. The goal of expanding and simplifying an expression is to make it easier to work with and understand.

The Importance of Expanding and Simplifying Algebraic Expressions

Expanding and simplifying algebraic expressions is essential in mathematics because it allows us to:

Simplify complex expressions: By expanding and simplifying expressions, we can make them easier to work with and understand.
Combine like terms: Expanding and simplifying expressions helps us to combine like terms, which can make it easier to solve equations and inequalities.
Solve equations and inequalities: Expanding and simplifying expressions is a crucial step in solving equations and inequalities.

Step 1: Expand the Expression

To expand the expression $(a - 4)(a + 8)$ , we need to multiply the two binomials. We can do this by using the FOIL method, which stands for "First, Outer, Inner, Last". This method involves multiplying the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

Using the FOIL Method

Using the FOIL method, we can expand the expression as follows:

First: Multiply the first terms of each binomial: $a \cdot a = a^2$
Outer: Multiply the outer terms of each binomial: $a \cdot 8 = 8a$
Inner: Multiply the inner terms of each binomial: $-4 \cdot a = -4a$
Last: Multiply the last terms of each binomial: $-4 \cdot 8 = -32$

Combining Like Terms

Now that we have expanded the expression, we can combine like terms. We can do this by adding or subtracting terms that have the same variable and exponent.

Combine like terms: $a^2 + 8a - 4a - 32 = a^2 + 4a - 32$

Step 2: Simplify the Expression

Now that we have expanded and combined like terms, we can simplify the expression. We can do this by rewriting the expression in a simpler form.

Simplify the expression: $a^2 + 4a - 32$

Conclusion

Expanding and simplifying algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, readers can learn how to expand and simplify expressions like $(a - 4)(a + 8)$ . We hope that this article has provided a clear and concise guide to expanding and simplifying algebraic expressions.

Common Mistakes to Avoid

When expanding and simplifying algebraic expressions, there are several common mistakes to avoid. These include:

Forgetting to combine like terms: Make sure to combine like terms when expanding and simplifying expressions.
Making errors when multiplying: Double-check your work when multiplying terms.
Not simplifying the expression: Make sure to simplify the expression after expanding and combining like terms.

Practice Problems

To practice expanding and simplifying algebraic expressions, try the following problems:

Problem 1: Expand and simplify the expression $(x + 2)(x - 3)$ .
Problem 2: Expand and simplify the expression $(2x - 1)(x + 4)$ .
Problem 3: Expand and simplify the expression $(x - 2)(x + 5)$ .

Final Thoughts

Introduction

Expanding and simplifying algebraic expressions is a crucial skill for students to master. In our previous article, we provided a step-by-step guide on how to expand and simplify expressions like $(a - 4)(a + 8)$ . In this article, we will answer some of the most frequently asked questions about expanding and simplifying algebraic expressions.

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

A: Expanding an expression involves multiplying the terms together, while simplifying an expression involves rewriting the expression in a simpler form by combining like terms.

Q: How do I know when to expand and simplify an expression?

A: You should expand an expression when you need to multiply the terms together, and simplify an expression when you need to rewrite the expression in a simpler form by combining like terms.

Q: What is the FOIL method, and how do I use it to expand expressions?

A: The FOIL method is a technique used to expand expressions by multiplying the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms. To use the FOIL method, simply multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

Q: How do I combine like terms when expanding and simplifying expressions?

A: To combine like terms, simply add or subtract the terms that have the same variable and exponent.

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

A: Some common mistakes to avoid when expanding and simplifying expressions include forgetting to combine like terms, making errors when multiplying, and not simplifying the expression.

Q: How can I practice expanding and simplifying expressions?

A: You can practice expanding and simplifying expressions by trying the practice problems at the end of our previous article, or by working on your own problems.

Q: What are some real-world applications of expanding and simplifying expressions?

A: Expanding and simplifying expressions has many real-world applications, including solving equations and inequalities, graphing functions, and modeling real-world situations.

Q: Can I use a calculator to expand and simplify expressions?

A: While a calculator can be a useful tool for expanding and simplifying expressions, it is not always necessary. In fact, using a calculator can sometimes make it more difficult to understand the underlying math.

Q: How can I check my work when expanding and simplifying expressions?

A: To check your work, simply re-read the problem and make sure that you have expanded and simplified the expression correctly.

Q: What are some tips for mastering the skill of expanding and simplifying expressions?

A: Some tips for mastering the skill of expanding and simplifying expressions include practicing regularly, paying attention to detail, and using the FOIL method to expand expressions.

Conclusion

Expanding and simplifying algebraic expressions is a crucial skill for students to master. By following the steps outlined in our previous article and answering the frequently asked questions in this article, readers can learn how to expand and simplify expressions like $(a - 4)(a + 8)$ . We hope that this article has provided a clear and concise guide to expanding and simplifying algebraic expressions.

Additional Resources

For additional resources on expanding and simplifying algebraic expressions, including practice problems and video tutorials, please visit our website.

Practice Problems

To practice expanding and simplifying algebraic expressions, try the following problems:

Problem 1: Expand and simplify the expression $(x + 2)(x - 3)$ .
Problem 2: Expand and simplify the expression $(2x - 1)(x + 4)$ .
Problem 3: Expand and simplify the expression $(x - 2)(x + 5)$ .