Express As A Trinomial: { (2x + 8)(3x - 7)$}$

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Introduction

In algebra, a trinomial is a polynomial expression consisting of three terms. When we are given a product of two binomials, we can expand it to obtain a trinomial. In this article, we will learn how to expand the given expression (2x+8)(3x−7){(2x + 8)(3x - 7)} into a trinomial.

Understanding the Concept of FOIL Method

To expand the given expression, we will use the FOIL method, which stands for First, Outer, Inner, Last. This method is used to multiply two binomials. The FOIL method states that we multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

Step 1: Multiply the First Terms

The first term of the first binomial is 2x, and the first term of the second binomial is 3x. We multiply these two terms to get:

2x * 3x = 6x^2

Step 2: Multiply the Outer Terms

The outer terms are 2x and -7. We multiply these two terms to get:

2x * -7 = -14x

Step 3: Multiply the Inner Terms

The inner terms are 8 and 3x. We multiply these two terms to get:

8 * 3x = 24x

Step 4: Multiply the Last Terms

The last terms are 8 and -7. We multiply these two terms to get:

8 * -7 = -56

Combining the Terms

Now that we have multiplied all the terms, we can combine them to get the expanded trinomial:

6x^2 - 14x + 24x - 56

Simplifying the Trinomial

We can simplify the trinomial by combining like terms. The like terms are -14x and 24x, which can be combined to get:

10x

So, the simplified trinomial is:

6x^2 + 10x - 56

Conclusion

In this article, we learned how to expand the given expression (2x+8)(3x−7){(2x + 8)(3x - 7)} into a trinomial using the FOIL method. We multiplied the first terms, then the outer terms, then the inner terms, and finally the last terms. We then combined the terms to get the expanded trinomial and simplified it by combining like terms.

Example Problems

Here are some example problems that you can try to practice expanding trinomials:

  1. (x+3)(2x−4){(x + 3)(2x - 4)}
  2. (x−2)(x+5){(x - 2)(x + 5)}
  3. (2x+1)(x−3){(2x + 1)(x - 3)}

Tips and Tricks

Here are some tips and tricks that you can use to help you expand trinomials:

  1. Use the FOIL method to multiply the binomials.
  2. Multiply the first terms, then the outer terms, then the inner terms, and finally the last terms.
  3. Combine like terms to simplify the trinomial.
  4. Check your work by plugging in values for x to see if the expression is true.

Common Mistakes

Here are some common mistakes that you can make when expanding trinomials:

  1. Not using the FOIL method to multiply the binomials.
  2. Not combining like terms to simplify the trinomial.
  3. Not checking your work by plugging in values for x to see if the expression is true.

Real-World Applications

Expanding trinomials has many real-world applications, including:

  1. Science: Expanding trinomials can be used to model real-world phenomena, such as the motion of objects under the influence of gravity.
  2. Engineering: Expanding trinomials can be used to design and optimize systems, such as electrical circuits and mechanical systems.
  3. Finance: Expanding trinomials can be used to model and analyze financial data, such as stock prices and interest rates.

Conclusion

Introduction

In our previous article, we learned how to expand a trinomial using the FOIL method. In this article, we will answer some frequently asked questions about expanding trinomials.

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 it involves multiplying the first terms, then the outer terms, then the inner terms, and finally the last terms.

Q: How do I use the FOIL method to expand a trinomial?

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

  1. Multiply the first terms of each binomial.
  2. Multiply the outer terms of each binomial.
  3. Multiply the inner terms of each binomial.
  4. Multiply the last terms of each binomial.
  5. Combine the terms to get the expanded trinomial.

Q: What are like terms?

A: Like terms are terms that have the same variable and coefficient. For example, 2x and 4x are like terms because they both have the variable x and the coefficient 2 and 4 respectively.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, if you have 2x + 4x, you can combine them to get 6x.

Q: What are some common mistakes to avoid when expanding trinomials?

A: Some common mistakes to avoid when expanding trinomials include:

  • Not using the FOIL method to multiply the binomials.
  • Not combining like terms to simplify the trinomial.
  • Not checking your work by plugging in values for x to see if the expression is true.

Q: How do I check my work when expanding a trinomial?

A: To check your work, plug in values for x and see if the expression is true. For example, if you have the trinomial 2x^2 + 3x - 4, you can plug in x = 1 to get 2(1)^2 + 3(1) - 4 = 2 + 3 - 4 = 1. If the expression is true, then your work is correct.

Q: What are some real-world applications of expanding trinomials?

A: Expanding trinomials has many real-world applications, including:

  • Science: Expanding trinomials can be used to model real-world phenomena, such as the motion of objects under the influence of gravity.
  • Engineering: Expanding trinomials can be used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Finance: Expanding trinomials can be used to model and analyze financial data, such as stock prices and interest rates.

Q: How can I practice expanding trinomials?

A: You can practice expanding trinomials by working through example problems and exercises. You can also use online resources, such as math websites and apps, to practice expanding trinomials.

Q: What are some tips for mastering the skill of expanding trinomials?

A: Some tips for mastering the skill of expanding trinomials include:

  • Practice regularly: Practice expanding trinomials regularly to build your skills and confidence.
  • Use the FOIL method: Use the FOIL method to multiply the binomials and simplify the trinomial.
  • Check your work: Check your work by plugging in values for x to see if the expression is true.
  • Seek help when needed: Seek help from a teacher or tutor if you are struggling with expanding trinomials.

Conclusion

In conclusion, expanding trinomials is an important concept in algebra that has many real-world applications. By using the FOIL method and combining like terms, we can simplify trinomials and make them easier to work with. With practice and patience, you can become proficient in expanding trinomials and apply this skill to a wide range of problems.