Simplify The Expression:$ A - 3\sqrt{2} + \sqrt{2} $

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to solve problems more efficiently and accurately. It involves combining like terms, removing unnecessary components, and rewriting the expression in a simpler form. In this article, we will focus on simplifying the given expression: $a - 3\sqrt{2} + \sqrt{2}$. We will break down the steps involved in simplifying this expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is $a - 3\sqrt{2} + \sqrt{2}$. This expression consists of three terms: $a$, $-3\sqrt{2}$, and $\sqrt{2}$. The first term is a simple variable $a$, while the second and third terms involve square roots.

Simplifying the Expression

To simplify the expression, we need to combine like terms. In this case, the like terms are the terms that involve the square root of 2. We can combine the two terms that involve the square root of 2 by adding their coefficients.

Combining Like Terms

The two terms that involve the square root of 2 are $-3\sqrt{2}$ and $\sqrt{2}$. We can combine these terms by adding their coefficients:

$$-3\sqrt{2} + \sqrt{2} = (-3 + 1)\sqrt{2} = -2\sqrt{2}$$

Now, we can rewrite the original expression with the combined like terms:

$$a - 3\sqrt{2} + \sqrt{2} = a - 2\sqrt{2}$$

Final Simplified Expression

The final simplified expression is $a - 2\sqrt{2}$. This expression is simpler than the original expression because it has fewer terms and no unnecessary components.

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us to solve problems more efficiently and accurately. In this article, we simplified the expression $a - 3\sqrt{2} + \sqrt{2}$ by combining like terms and removing unnecessary components. The final simplified expression is $a - 2\sqrt{2}$. We hope that this article has provided a clear explanation of the steps involved in simplifying this expression and has helped you to understand the importance of simplifying expressions in mathematics.

Frequently Asked Questions

• What is the final simplified expression of $a - 3\sqrt{2} + \sqrt{2}$?
• How do you combine like terms in an expression?
• What is the importance of simplifying expressions in mathematics?

Answer 1: Final Simplified Expression

The final simplified expression of $a - 3\sqrt{2} + \sqrt{2}$ is $a - 2\sqrt{2}$.

Answer 2: Combining Like Terms

To combine like terms in an expression, you need to add or subtract the coefficients of the like terms. In the case of the expression $a - 3\sqrt{2} + \sqrt{2}$, we combined the two terms that involve the square root of 2 by adding their coefficients.

Answer 3: Importance of Simplifying Expressions

Simplifying expressions is important in mathematics because it helps us to solve problems more efficiently and accurately. By simplifying expressions, we can remove unnecessary components and combine like terms, making it easier to work with the expression and arrive at the correct solution.

Additional Resources

• Simplifying Expressions
• Combining Like Terms
• Simplifying Algebraic Expressions

Related Topics

• Simplifying Fractions
• Simplifying Rational Expressions
• Simplifying Radical Expressions
  

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Introduction

In our previous article, we simplified the expression $a - 3\sqrt{2} + \sqrt{2}$ by combining like terms and removing unnecessary components. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional resources for further learning.

Q&A

Q1: What is the final simplified expression of $a - 3\sqrt{2} + \sqrt{2}$?

A1: The final simplified expression of $a - 3\sqrt{2} + \sqrt{2}$ is $a - 2\sqrt{2}$.

Q2: How do you combine like terms in an expression?

A2: To combine like terms in an expression, you need to add or subtract the coefficients of the like terms. In the case of the expression $a - 3\sqrt{2} + \sqrt{2}$, we combined the two terms that involve the square root of 2 by adding their coefficients.

Q3: What is the importance of simplifying expressions in mathematics?

A3: Simplifying expressions is important in mathematics because it helps us to solve problems more efficiently and accurately. By simplifying expressions, we can remove unnecessary components and combine like terms, making it easier to work with the expression and arrive at the correct solution.

Q4: Can you provide an example of a more complex expression that can be simplified?

A4: Yes, here is an example of a more complex expression that can be simplified:

$$2x^2 + 5x - 3 - 2x^2 + 2x$$

To simplify this expression, we can combine like terms:

$$2x^2 + 5x - 3 - 2x^2 + 2x = 5x - 3 + 2x = 7x - 3$$

Q5: How do you simplify expressions with variables in the denominator?

A5: To simplify expressions with variables in the denominator, you need to follow the order of operations (PEMDAS) and simplify the expression inside the denominator first. For example:

$$\frac{2x + 3}{x - 2}$$

To simplify this expression, we can start by simplifying the expression inside the denominator:

$$x - 2 = x - 2$$

Then, we can simplify the expression by dividing the numerator by the denominator:

$$\frac{2x + 3}{x - 2} = \frac{2x + 3}{x - 2} \times \frac{x + 2}{x + 2} = \frac{2x^2 + 7x + 6}{x^2 - 4}$$

Q6: Can you provide additional resources for learning about simplifying expressions?

A6: Yes, here are some additional resources for learning about simplifying expressions:

• Simplifying Expressions
• Combining Like Terms
• Simplifying Algebraic Expressions

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us to solve problems more efficiently and accurately. By combining like terms and removing unnecessary components, we can simplify expressions and arrive at the correct solution. We hope that this article has provided a clear explanation of the steps involved in simplifying expressions and has helped you to understand the importance of simplifying expressions in mathematics.

Frequently Asked Questions

• What is the final simplified expression of $a - 3\sqrt{2} + \sqrt{2}$?
• How do you combine like terms in an expression?
• What is the importance of simplifying expressions in mathematics?
• Can you provide an example of a more complex expression that can be simplified?
• How do you simplify expressions with variables in the denominator?
• Can you provide additional resources for learning about simplifying expressions?

Answer 1: Final Simplified Expression

The final simplified expression of $a - 3\sqrt{2} + \sqrt{2}$ is $a - 2\sqrt{2}$.

Answer 2: Combining Like Terms

To combine like terms in an expression, you need to add or subtract the coefficients of the like terms. In the case of the expression $a - 3\sqrt{2} + \sqrt{2}$, we combined the two terms that involve the square root of 2 by adding their coefficients.

Answer 3: Importance of Simplifying Expressions

Simplifying expressions is important in mathematics because it helps us to solve problems more efficiently and accurately. By simplifying expressions, we can remove unnecessary components and combine like terms, making it easier to work with the expression and arrive at the correct solution.

Answer 4: Example of a More Complex Expression

Here is an example of a more complex expression that can be simplified:

$$2x^2 + 5x - 3 - 2x^2 + 2x$$

To simplify this expression, we can combine like terms:

$$2x^2 + 5x - 3 - 2x^2 + 2x = 5x - 3 + 2x = 7x - 3$$

Answer 5: Simplifying Expressions with Variables in the Denominator

To simplify expressions with variables in the denominator, you need to follow the order of operations (PEMDAS) and simplify the expression inside the denominator first. For example:

$$\frac{2x + 3}{x - 2}$$

To simplify this expression, we can start by simplifying the expression inside the denominator:

$$x - 2 = x - 2$$

Then, we can simplify the expression by dividing the numerator by the denominator:

$$\frac{2x + 3}{x - 2} = \frac{2x + 3}{x - 2} \times \frac{x + 2}{x + 2} = \frac{2x^2 + 7x + 6}{x^2 - 4}$$

Answer 6: Additional Resources

Yes, here are some additional resources for learning about simplifying expressions:

• Simplifying Expressions
• Combining Like Terms
• Simplifying Algebraic Expressions