Jared And Maliyah Are Working On The Same Problem. Is Either Of Them Correct? Explain Your Reasoning.Jared:$\[ \begin{aligned} (3x-1)(x+1) & = 3x^2 + 3x - X - 1 \\ & = 3x^2 + 2x - 1 \end{aligned} \\]Maliyah:$\[ \begin{aligned} (3x-1)(x+1)

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Multiplying Binomials: A Comparison of Jared and Maliyah's Work

In mathematics, the process of multiplying binomials is a fundamental concept that students often encounter in algebra. When multiplying binomials, it's essential to follow the correct order of operations to ensure that the resulting expression is accurate. In this article, we will examine the work of Jared and Maliyah as they attempt to multiply the binomials (3x-1) and (x+1). We will compare their approaches and determine which one is correct.

Jared's work on multiplying the binomials (3x-1) and (x+1) is as follows:

{ \begin{aligned} (3x-1)(x+1) & = 3x^2 + 3x - x - 1 \\ & = 3x^2 + 2x - 1 \end{aligned} \}

At first glance, Jared's work appears to be correct. However, let's take a closer look at the steps he followed. Jared correctly multiplied the first terms of each binomial, which is 3x and x, resulting in 3x^2. He then multiplied the outer terms, which is 3x and 1, resulting in 3x. Next, he multiplied the inner terms, which is -1 and x, resulting in -x. Finally, he multiplied the last terms, which is -1 and 1, resulting in -1.

However, Jared made a mistake when he combined the terms 3x and -x. He incorrectly added them together, resulting in 2x. The correct combination of these terms would be 3x - x = 2x, but Jared wrote it as 3x^2 + 2x - 1.

Maliyah's work on multiplying the binomials (3x-1) and (x+1) is as follows:

{ \begin{aligned} (3x-1)(x+1) & = (3x)(x) + (3x)(1) + (-1)(x) + (-1)(1) \\ & = 3x^2 + 3x - x - 1 \end{aligned} \}

Maliyah's approach is more detailed and explicit. She correctly multiplied each term of the first binomial by each term of the second binomial, resulting in four separate terms. She then combined like terms, which is 3x^2 and -x, resulting in 3x^2 - x. Finally, she combined the constants, which is -1 and -1, resulting in -2.

Now that we have examined both Jared and Maliyah's work, let's compare their approaches. Jared's work is more concise, but it contains a mistake. Maliyah's work is more detailed and explicit, but it is also more time-consuming.

In terms of accuracy, Maliyah's work is correct, while Jared's work is incorrect. Maliyah correctly multiplied each term of the first binomial by each term of the second binomial, resulting in four separate terms. She then combined like terms and constants correctly, resulting in the final expression 3x^2 + 2x - 1.

In conclusion, Jared and Maliyah's work on multiplying the binomials (3x-1) and (x+1) demonstrates the importance of following the correct order of operations and being explicit in one's work. While Jared's work is more concise, it contains a mistake. Maliyah's work, on the other hand, is more detailed and explicit, but it is also more time-consuming. Ultimately, the correct approach is the one that results in an accurate expression.

When multiplying binomials, it's essential to follow the correct order of operations. Here are some tips to help you multiply binomials correctly:

  • Multiply each term of the first binomial by each term of the second binomial.
  • Combine like terms.
  • Combine constants.
  • Be explicit in your work and show all the steps.

By following these tips, you can ensure that your work is accurate and that you are multiplying binomials correctly.

When multiplying binomials, there are several common mistakes to avoid. Here are some of the most common mistakes:

  • Not multiplying each term of the first binomial by each term of the second binomial.
  • Not combining like terms.
  • Not combining constants.
  • Being too concise and not showing all the steps.

By avoiding these common mistakes, you can ensure that your work is accurate and that you are multiplying binomials correctly.

Multiplying binomials has several real-world applications. Here are some examples:

  • In physics, multiplying binomials is used to calculate the velocity of an object.
  • In engineering, multiplying binomials is used to calculate the stress on a material.
  • In economics, multiplying binomials is used to calculate the cost of a product.

By understanding how to multiply binomials, you can apply this concept to real-world problems and make informed decisions.

Multiplying binomials is a fundamental concept in mathematics that has several real-world applications. In our previous article, we examined the work of Jared and Maliyah as they attempted to multiply the binomials (3x-1) and (x+1). We compared their approaches and determined which one was correct. In this article, we will provide a Q&A guide to help you understand how to multiply binomials correctly.

A binomial is an algebraic expression that consists of two terms. For example, (3x-1) and (x+1) are both binomials.

To multiply binomials, you need to follow the correct order of operations. Here are the steps:

  1. Multiply each term of the first binomial by each term of the second binomial.
  2. Combine like terms.
  3. Combine constants.

The correct order of operations is:

  1. Multiply each term of the first binomial by each term of the second binomial.
  2. Combine like terms.
  3. Combine constants.

To combine like terms, you need to add or subtract the coefficients of the terms that have the same variable. For example, if you have the terms 3x and 2x, you can combine them by adding their coefficients, resulting in 5x.

To combine constants, you need to add or subtract the constants. For example, if you have the constants 3 and 2, you can combine them by adding them, resulting in 5.

Some common mistakes to avoid when multiplying binomials include:

  • Not multiplying each term of the first binomial by each term of the second binomial.
  • Not combining like terms.
  • Not combining constants.
  • Being too concise and not showing all the steps.

Multiplying binomials has several real-world applications. Here are some examples:

  • In physics, multiplying binomials is used to calculate the velocity of an object.
  • In engineering, multiplying binomials is used to calculate the stress on a material.
  • In economics, multiplying binomials is used to calculate the cost of a product.

Here are some tips for multiplying binomials correctly:

  • Be explicit in your work and show all the steps.
  • Use the correct order of operations.
  • Combine like terms and constants correctly.
  • Avoid common mistakes.

In conclusion, multiplying binomials is a fundamental concept in mathematics that has several real-world applications. By following the correct order of operations and being explicit in one's work, you can ensure that your work is accurate and that you are multiplying binomials correctly. Remember to avoid common mistakes and to be concise in your work. With practice and patience, you can become proficient in multiplying binomials and apply this concept to real-world problems.

If you need additional help with multiplying binomials, here are some additional resources:

  • Online tutorials and videos
  • Algebra textbooks and workbooks
  • Online practice problems and quizzes

By using these resources, you can improve your understanding of how to multiply binomials correctly and apply this concept to real-world problems.