Multiply \[$(3x + 1)(x - 1)\$\].Express The Answer In Standard Form.Enter Your Answer In The Box: \[$\square\$\]
Introduction
In algebra, multiplying expressions is a fundamental operation that helps us simplify complex equations and solve problems. In this article, we will focus on multiplying the expression {(3x + 1)(x - 1)$}$ and express the answer in standard form.
Understanding the Expression
Before we start multiplying, let's break down the given expression:
{(3x + 1)(x - 1)$}$
This expression consists of two binomials, ${3x + 1\$} and {x - 1$}$, which are being multiplied together.
Multiplying Binomials
To multiply binomials, we can use the FOIL method, which stands for First, Outer, Inner, Last. This method helps us multiply the first terms, then the outer terms, then the inner terms, and finally the last terms.
Step 1: Multiply the First Terms
The first terms are ${3x\$} and {x$}$. When we multiply these two terms, we get:
${3x \cdot x = 3x^2\$}
Step 2: Multiply the Outer Terms
The outer terms are ${3x\$} and {-1$}$. When we multiply these two terms, we get:
${3x \cdot -1 = -3x\$}
Step 3: Multiply the Inner Terms
The inner terms are ${1\$} and {x$}$. When we multiply these two terms, we get:
${1 \cdot x = x\$}
Step 4: Multiply the Last Terms
The last terms are ${1\$} and {-1$}$. When we multiply these two terms, we get:
${1 \cdot -1 = -1\$}
Combining the Terms
Now that we have multiplied all the terms, let's combine them:
${3x^2 - 3x + x - 1\$}
We can simplify this expression by combining like terms:
${3x^2 - 2x - 1\$}
Conclusion
In this article, we multiplied the expression {(3x + 1)(x - 1)$}$ using the FOIL method and expressed the answer in standard form. We broke down the expression into smaller parts, multiplied each pair of terms, and then combined the results to get the final answer.
Key Takeaways
- Multiplying binomials involves using the FOIL method to multiply the first terms, then the outer terms, then the inner terms, and finally the last terms.
- Combining like terms is an essential step in simplifying algebraic expressions.
- Standard form is an important concept in algebra, as it helps us express complex expressions in a clear and concise manner.
Practice Problems
Try multiplying the following expressions using the FOIL method:
- {(2x + 3)(x + 4)$}$
- {(x - 2)(x + 5)$}$
- {(3x - 1)(x + 2)$}$
Answer Key
- {(2x + 3)(x + 4) = 2x^2 + 13x + 12$}$
- {(x - 2)(x + 5) = x^2 + 3x - 10$}$
- {(3x - 1)(x + 2) = 3x^2 + 5x - 2$}$
Additional Resources
For more practice problems and examples, check out the following resources:
- Khan Academy: Algebra
- Mathway: Algebra Calculator
- IXL: Algebra Practice
Multiplying Algebraic Expressions: A Q&A Guide =====================================================
Introduction
In our previous article, we explored the concept of multiplying algebraic expressions using the FOIL method. In this article, we will address some common questions and concerns that students may have when working with multiplying expressions.
Q&A
Q: What is the FOIL method?
A: The FOIL method is a technique used to multiply two binomials. It stands for First, Outer, Inner, Last, and involves multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms.
Q: Why do I need to use the FOIL method?
A: The FOIL method helps you to multiply binomials in a systematic and organized way. It ensures that you don't miss any terms and that you combine like terms correctly.
Q: Can I use the FOIL method for multiplying more than two binomials?
A: No, the FOIL method is specifically designed for multiplying two binomials. If you need to multiply more than two binomials, you will need to use a different method, such as the distributive property.
Q: How do I know when to combine like terms?
A: You should combine like terms when you have two or more terms that have the same variable and exponent. For example, in the expression ${3x^2 - 2x + x - 1\$}, you can combine the and terms to get .
Q: What is standard form?
A: Standard form is a way of expressing an algebraic expression in a clear and concise manner. It involves writing the expression in the form {ax^n + bx^m + \ldots$}$, where , , and , , etc. are constants and variables.
Q: Why is standard form important?
A: Standard form is important because it helps you to:
- Simplify complex expressions
- Compare expressions
- Solve equations
- Graph functions
Q: Can I use the FOIL method for multiplying expressions with variables and constants?
A: Yes, the FOIL method can be used for multiplying expressions with variables and constants. For example, in the expression {(2x + 3)(x + 4)$}$, you can use the FOIL method to multiply the terms and get ${2x^2 + 13x + 12\$}.
Q: What are some common mistakes to avoid when multiplying expressions?
A: Some common mistakes to avoid when multiplying expressions include:
- Forgetting to multiply all the terms
- Not combining like terms correctly
- Not using the correct order of operations
- Not checking your work for errors
Conclusion
In this article, we addressed some common questions and concerns that students may have when working with multiplying expressions. We covered topics such as the FOIL method, combining like terms, and standard form. We also provided some tips and reminders to help you avoid common mistakes.
Practice Problems
Try multiplying the following expressions using the FOIL method:
- {(2x + 3)(x + 4)$}$
- {(x - 2)(x + 5)$}$
- {(3x - 1)(x + 2)$}$
Answer Key
- {(2x + 3)(x + 4) = 2x^2 + 13x + 12$}$
- {(x - 2)(x + 5) = x^2 + 3x - 10$}$
- {(3x - 1)(x + 2) = 3x^2 + 5x - 2$}$
Additional Resources
For more practice problems and examples, check out the following resources:
- Khan Academy: Algebra
- Mathway: Algebra Calculator
- IXL: Algebra Practice