Express The Product { (2x - 1)(3x + 4)$}$ As A Trinomial:1. ${$5x^2 + 9x - 4$}$2. ${$5x - 4$}$3. ${$6x^2 - 5x - 4$}$4. ${ 6x^2 + 5x - 4\$}

Introduction

In algebra, a trinomial is a polynomial with three terms. Expressing a product as a trinomial involves multiplying two binomials to obtain a trinomial. In this article, we will explore how to express the product {(2x - 1)(3x + 4)$}$ as a trinomial.

Understanding the Product

To express the product {(2x - 1)(3x + 4)$}$ as a trinomial, we need to multiply the two binomials. This involves multiplying each term in the first binomial by each term in the second binomial.

Multiplying Binomials

To multiply binomials, we use the FOIL method, which stands for First, Outer, Inner, Last. This method involves multiplying the first terms in each binomial, then the outer terms, then the inner terms, and finally the last terms.

FOIL Method

• Multiply the first terms: ${2x \cdot 3x = 6x^2\$}
• Multiply the outer terms: ${2x \cdot 4 = 8x\$}
• Multiply the inner terms: {-1 \cdot 3x = -3x$}$
• Multiply the last terms: {-1 \cdot 4 = -4$}$

Combining Like Terms

Now that we have multiplied the binomials, we need to combine like terms. Like terms are terms that have the same variable raised to the same power.

Combining Like Terms

• Combine the terms with the same variable raised to the same power: ${6x^2 + 8x - 3x - 4\$}
• Simplify the expression by combining like terms: ${6x^2 + 5x - 4\$}

Conclusion

In this article, we have explored how to express the product {(2x - 1)(3x + 4)$}$ as a trinomial. We used the FOIL method to multiply the binomials and then combined like terms to simplify the expression. The final answer is ${6x^2 + 5x - 4\$}.

Answer Options

Based on our calculation, the correct answer is:

• Option 4: ${6x^2 + 5x - 4\$}

Why is this the correct answer?

This is the correct answer because we used the FOIL method to multiply the binomials and then combined like terms to simplify the expression. The final answer matches one of the options provided.

Tips and Tricks

• When multiplying binomials, use the FOIL method to ensure that you multiply each term correctly.
• When combining like terms, simplify the expression by combining terms with the same variable raised to the same power.
• Practice multiplying binomials and combining like terms to become more comfortable with the process.

Common Mistakes

• Failing to use the FOIL method when multiplying binomials can lead to incorrect results.
• Failing to combine like terms can result in an expression that is not simplified.
• Not checking the final answer against the options provided can lead to selecting the incorrect answer.

Conclusion

Introduction

In our previous article, we explored how to express the product {(2x - 1)(3x + 4)$}$ as a trinomial. In this article, we will answer some common questions related to expressing a product as a trinomial.

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 in each binomial, then the outer terms, then the inner terms, and finally the last terms.

Q: How do I use the FOIL method?

A: To use the FOIL method, follow these steps:

1. Multiply the first terms: ${2x \cdot 3x = 6x^2\$}
2. Multiply the outer terms: ${2x \cdot 4 = 8x\$}
3. Multiply the inner terms: {-1 \cdot 3x = -3x$}$
4. Multiply the last terms: {-1 \cdot 4 = -4$}$

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or different powers of the same variable.

Q: How do I combine like terms?

A: To combine like terms, follow these steps:

1. Identify the like terms: ${6x^2 + 8x - 3x - 4\$}
2. Combine the like terms: ${6x^2 + 5x - 4\$}

Q: What is the final answer to the problem {(2x - 1)(3x + 4)$}$?

A: The final answer to the problem {(2x - 1)(3x + 4)$}$ is ${6x^2 + 5x - 4\$}.

Q: Why is it important to use the FOIL method when multiplying binomials?

A: Using the FOIL method when multiplying binomials ensures that you multiply each term correctly and obtain the correct answer.

Q: What are some common mistakes to avoid when expressing a product as a trinomial?

A: Some common mistakes to avoid when expressing a product as a trinomial include:

• Failing to use the FOIL method when multiplying binomials
• Failing to combine like terms
• Not checking the final answer against the options provided

Q: How can I practice expressing a product as a trinomial?

A: You can practice expressing a product as a trinomial by:

• Multiplying binomials using the FOIL method
• Combining like terms
• Checking the final answer against the options provided

Conclusion

In conclusion, expressing a product as a trinomial involves multiplying two binomials and then combining like terms to simplify the expression. By using the FOIL method and combining like terms, we can ensure that we obtain the correct answer. Practice multiplying binomials and combining like terms to become more comfortable with the process.

Additional Resources

• Algebra Tutorial
• [FOIL Method Tutorial](https://www.khanacademy.org/math/algebra/x2f-alg-1/x2f-alg-1-1/x2f-alg-1-1-1/x2f-alg-1-1-1-1/x2f-alg-1-1-1-1-1/x2f-alg-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1/x2f-alg-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-