Expand And Simplify { (2x+1)(x-2)(x+3)$}$.

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Introduction

In algebra, expanding and simplifying expressions is a crucial skill that helps us solve equations and manipulate mathematical expressions. In this article, we will focus on expanding and simplifying the given expression {(2x+1)(x-2)(x+3)$}$. We will use various techniques such as the distributive property and combining like terms to simplify the expression.

Understanding the Expression

Before we start expanding and simplifying the expression, let's first understand what it means. The expression {(2x+1)(x-2)(x+3)$}$ is a product of three binomials. A binomial is an algebraic expression consisting of two terms. In this case, we have three binomials multiplied together.

Expanding the Expression

To expand the expression, we will use the distributive property. The distributive property states that for any real numbers a, b, and c, we have:

a(b + c) = ab + ac

We can apply this property to each pair of binomials in the expression.

Step 1: Multiply the First Two Binomials

Let's start by multiplying the first two binomials: {(2x+1)$) and [(x-2)\$}.

{(2x+1)(x-2) = 2x^2 - 4x + x - 2}$

Using the distributive property, we can simplify this expression to:

${2x^2 - 3x - 2}

Step 2: Multiply the Result by the Third Binomial

Now, let's multiply the result by the third binomial: {(x+3)$}$.

{(2x^2 - 3x - 2)(x+3) = 2x^3 + 6x^2 - 3x^2 - 9x - 2x - 6}$

Using the distributive property, we can simplify this expression to:

${2x^3 + 3x^2 - 11x - 6}

Simplifying the Expression

Now that we have expanded the expression, let's simplify it by combining like terms.

Combining Like Terms

We can combine like terms by adding or subtracting the coefficients of the same variables.

${2x^3 + 3x^2 - 11x - 6 = 2x^3 + 3x^2 - 11x - 6}

In this case, there are no like terms to combine.

Final Answer

The final answer is ${2x^3 + 3x^2 - 11x - 6}.

Conclusion

In this article, we expanded and simplified the given expression {(2x+1)(x-2)(x+3)$}$. We used the distributive property to multiply the binomials and combined like terms to simplify the expression. The final answer is ${2x^3 + 3x^2 - 11x - 6}.

Frequently Asked Questions

  • Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, we have: a(b + c) = ab + ac.
  • Q: How do I expand and simplify an expression? A: To expand and simplify an expression, you can use the distributive property to multiply the binomials and combine like terms.
  • Q: What are like terms? A: Like terms are terms that have the same variables and coefficients.

Further Reading

  • Algebra: A Comprehensive Introduction
  • Expanding and Simplifying Expressions
  • The Distributive Property

References

  • [1] Algebra: A Comprehensive Introduction by Michael Artin
  • [2] Expanding and Simplifying Expressions by Math Open Reference
  • [3] The Distributive Property by Khan Academy

Introduction

In our previous article, we expanded and simplified the given expression {(2x+1)(x-2)(x+3)$}$. We used the distributive property to multiply the binomials and combined like terms to simplify the expression. In this article, we will answer some frequently asked questions about expanding and simplifying expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, we have: a(b + c) = ab + ac. This property allows us to multiply a single term by a binomial.

Q: How do I expand and simplify an expression?

A: To expand and simplify an expression, you can use the distributive property to multiply the binomials and combine like terms. Here's a step-by-step guide:

  1. Multiply the first two binomials using the distributive property.
  2. Multiply the result by the third binomial using the distributive property.
  3. Combine like terms to simplify the expression.

Q: What are like terms?

A: Like terms are terms that have the same variables and coefficients. 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, you can add or subtract the coefficients of the same variables. For example, 2x + 4x = 6x.

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

A: Expanding an expression means multiplying the binomials using the distributive property, while simplifying an expression means combining like terms to reduce the expression to its simplest form.

Q: Can I simplify an expression without expanding it?

A: Yes, you can simplify an expression without expanding it. For example, if you have the expression 2x + 4x, you can simplify it by combining like terms: 2x + 4x = 6x.

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

A: You should expand and simplify an expression when you need to manipulate the expression to solve an equation or to make it easier to work with.

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

A: Yes, you can use a calculator to expand and simplify an expression. However, it's always a good idea to check your work by hand to make sure you understand the process.

Conclusion

In this article, we answered some frequently asked questions about expanding and simplifying expressions. We covered topics such as the distributive property, combining like terms, and when to expand and simplify an expression. We hope this article has been helpful in clarifying any confusion you may have had about expanding and simplifying expressions.

Frequently Asked Questions

  • Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, we have: a(b + c) = ab + ac.
  • Q: How do I expand and simplify an expression? A: To expand and simplify an expression, you can use the distributive property to multiply the binomials and combine like terms.
  • Q: What are like terms? A: Like terms are terms that have the same variables and coefficients.

Further Reading

  • Algebra: A Comprehensive Introduction
  • Expanding and Simplifying Expressions
  • The Distributive Property

References

  • [1] Algebra: A Comprehensive Introduction by Michael Artin
  • [2] Expanding and Simplifying Expressions by Math Open Reference
  • [3] The Distributive Property by Khan Academy