Rewrite The Expression In Expanded Form: $2(x+3)^2$

by ADMIN 54 views

Introduction

In algebra, expanding an expression means rewriting it in a form where all the terms are multiplied out. This is an essential skill in mathematics, as it allows us to simplify and manipulate expressions more easily. In this article, we will focus on rewriting the expression 2(x+3)^2 in expanded form.

Understanding the Expression

Before we begin, let's take a closer look at the expression 2(x+3)^2. This expression consists of two main parts: the coefficient 2 and the binomial (x+3)^2. The binomial (x+3)^2 is a squared expression, which means it is the result of multiplying the binomial (x+3) by itself.

Expanding the Binomial

To expand the binomial (x+3)^2, we need to use the formula (a+b)^2 = a^2 + 2ab + b^2. In this case, a = x and b = 3. Plugging these values into the formula, we get:

(x+3)^2 = x^2 + 2(x)(3) + 3^2

Simplifying the Expression

Now that we have expanded the binomial, we can simplify the expression 2(x+3)^2. To do this, we need to multiply the coefficient 2 by the expanded binomial:

2(x+3)^2 = 2(x^2 + 6x + 9)

Distributing the Coefficient

To distribute the coefficient 2, we need to multiply it by each term in the expanded binomial:

2(x^2 + 6x + 9) = 2x^2 + 2(6x) + 2(9)

Simplifying the Terms

Now that we have distributed the coefficient, we can simplify the terms:

2x^2 + 12x + 18

Conclusion

In this article, we have rewritten the expression 2(x+3)^2 in expanded form. We started by understanding the expression and identifying the binomial (x+3)^2. We then expanded the binomial using the formula (a+b)^2 = a^2 + 2ab + b^2. Finally, we simplified the expression by distributing the coefficient 2 and combining like terms. The final answer is 2x^2 + 12x + 18.

Example Use Cases

Rewriting expressions in expanded form is an essential skill in mathematics, and it has many practical applications. Here are a few example use cases:

  • Simplifying expressions: By rewriting expressions in expanded form, we can simplify them and make them easier to work with.
  • Factoring expressions: By rewriting expressions in expanded form, we can also factor them and identify their roots.
  • Solving equations: By rewriting expressions in expanded form, we can solve equations more easily and accurately.

Tips and Tricks

Here are a few tips and tricks to help you rewrite expressions in expanded form:

  • Use the formula (a+b)^2 = a^2 + 2ab + b^2: This formula is essential for expanding binomials.
  • Distribute the coefficient: When distributing the coefficient, make sure to multiply it by each term in the expanded binomial.
  • Combine like terms: When simplifying the expression, combine like terms to make it easier to work with.

Conclusion

Introduction

In our previous article, we discussed how to rewrite the expression 2(x+3)^2 in expanded form. In this article, we will answer some frequently asked questions about rewriting expressions in expanded form.

Q: What is the formula for expanding a binomial?

A: The formula for expanding a binomial is (a+b)^2 = a^2 + 2ab + b^2. This formula can be used to expand any binomial.

Q: How do I distribute the coefficient when rewriting an expression in expanded form?

A: When distributing the coefficient, you need to multiply it by each term in the expanded binomial. For example, if you have the expression 2(x+3)^2, you would multiply the coefficient 2 by each term in the expanded binomial: 2x^2 + 2(6x) + 2(9).

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

A: Expanding an expression means rewriting it in a form where all the terms are multiplied out. Factoring an expression means rewriting it in a form where it is expressed as a product of simpler expressions.

Q: Can I use the formula (a+b)^2 = a^2 + 2ab + b^2 to expand any binomial?

A: Yes, you can use the formula (a+b)^2 = a^2 + 2ab + b^2 to expand any binomial. However, you need to make sure that the binomial is in the form (a+b)^2.

Q: How do I simplify an expression after rewriting it in expanded form?

A: To simplify an expression after rewriting it in expanded form, you need to combine like terms. Like terms are terms that have the same variable and exponent.

Q: What are some common mistakes to avoid when rewriting expressions in expanded form?

A: Some common mistakes to avoid when rewriting expressions in expanded form include:

  • Not using the correct formula: Make sure to use the correct formula for expanding a binomial.
  • Not distributing the coefficient correctly: Make sure to multiply the coefficient by each term in the expanded binomial.
  • Not combining like terms: Make sure to combine like terms to simplify the expression.

Q: Can I use a calculator to rewrite expressions in expanded form?

A: Yes, you can use a calculator to rewrite expressions in expanded form. However, it's always a good idea to double-check your work by hand to make sure that you understand the process.

Q: How do I know if I have rewritten an expression in expanded form correctly?

A: To check if you have rewritten an expression in expanded form correctly, you can plug the expression into a calculator and see if it simplifies to the correct answer. You can also check your work by hand by multiplying out the terms and combining like terms.

Conclusion

Rewriting expressions in expanded form is an essential skill in mathematics, and it has many practical applications. By understanding the formula for expanding a binomial, distributing the coefficient, and simplifying the expression, you can rewrite expressions in expanded form. We hope that this Q&A article has helped to clarify any questions you may have had about rewriting expressions in expanded form.