Simplify \[$-2xy + 3x - 2xy + 3x\$\].A. \[$4xy + 6x\$\] B. \[$4xy - 6x\$\] C. \[$-4xy + 6x\$\] D. \[$2xy\$\]

Understanding the Basics of Algebraic Simplification

Algebraic simplification is a crucial concept in mathematics that involves reducing complex expressions to their simplest form. This process helps in solving equations, inequalities, and other mathematical problems efficiently. In this article, we will focus on simplifying a given algebraic expression, {-2xy + 3x - 2xy + 3x$}$.

The Given Expression: {-2xy + 3x - 2xy + 3x$}$

The given expression is a combination of two terms, each containing variables and constants. To simplify this expression, we need to apply the rules of algebraic operations.

Step 1: Combine Like Terms

Like terms are terms that have the same variable(s) raised to the same power. In the given expression, we can identify two like terms: ${-2xy}$ and ${-2xy}$, and ${3x}$ and ${3x}$. We can combine these like terms by adding or subtracting their coefficients.

Combining Like Terms: ${-2xy + 3x - 2xy + 3x}$

To combine like terms, we add or subtract the coefficients of the like terms. In this case, we have:

${-2xy + 3x - 2xy + 3x}$

We can combine the like terms as follows:

${-2xy - 2xy + 3x + 3x}$

Now, we can add the coefficients of the like terms:

${-4xy + 6x}$

Simplified Expression: ${-4xy + 6x}$

The simplified expression is ${-4xy + 6x}$. This is the final answer.

Comparing the Simplified Expression with the Options

Now, let's compare the simplified expression with the given options:

A. ${4xy + 6x}$ B. ${4xy - 6x}$ C. ${-4xy + 6x}$ D. ${2xy}$

The simplified expression ${-4xy + 6x}$ matches option C.

Conclusion

In this article, we simplified the given algebraic expression ${-2xy + 3x - 2xy + 3x}$ by combining like terms. The simplified expression is ${-4xy + 6x}$. This process demonstrates the importance of algebraic simplification in solving mathematical problems efficiently.

Frequently Asked Questions

Q: What is algebraic simplification?

A: Algebraic simplification is the process of reducing complex algebraic expressions to their simplest form.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms by adding or subtracting their coefficients.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power.

Q: Why is algebraic simplification important?

A: Algebraic simplification is important because it helps in solving equations, inequalities, and other mathematical problems efficiently.

Additional Resources

For more information on algebraic simplification, you can refer to the following resources:

• Khan Academy: Algebraic Simplification
• Mathway: Algebraic Simplification
• Wolfram Alpha: Algebraic Simplification

Final Answer

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Understanding Algebraic Simplification

Algebraic simplification is a crucial concept in mathematics that involves reducing complex expressions to their simplest form. This process helps in solving equations, inequalities, and other mathematical problems efficiently. In this article, we will address some frequently asked questions about algebraic simplification.

Q: What is algebraic simplification?

A: Algebraic simplification is the process of reducing complex algebraic expressions to their simplest form. This involves combining like terms, removing parentheses, and rearranging the expression to make it easier to work with.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

1. Combine like terms: Identify and combine terms that have the same variable(s) raised to the same power.
2. Remove parentheses: Remove any parentheses that are not necessary for the expression.
3. Rearrange the expression: Rearrange the expression to make it easier to work with.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. For example, ${2x}$ and ${3x}$ are like terms because they both have the variable ${x}$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the expression ${2x + 3x}$, you can combine the like terms by adding the coefficients:

${2x + 3x = 5x}$

Q: What is the order of operations in algebraic simplification?

A: The order of operations in algebraic simplification is:

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I simplify an expression with variables in the denominator?

A: Yes, you can simplify an expression with variables in the denominator. However, you need to follow the rules of algebraic simplification carefully to avoid making mistakes.

Q: How do I simplify a fraction with variables in the numerator and denominator?

A: To simplify a fraction with variables in the numerator and denominator, you need to follow these steps:

1. Factor the numerator and denominator: Factor the numerator and denominator to identify any common factors.
2. Cancel out common factors: Cancel out any common factors between the numerator and denominator.
3. Simplify the expression: Simplify the expression by combining like terms.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients. However, you need to follow the rules of algebraic simplification carefully to avoid making mistakes.

Q: How do I simplify an expression with absolute value?

A: To simplify an expression with absolute value, you need to follow these steps:

1. Remove the absolute value sign: Remove the absolute value sign and evaluate the expression inside.
2. Simplify the expression: Simplify the expression by combining like terms.

Conclusion

Algebraic simplification is a crucial concept in mathematics that involves reducing complex expressions to their simplest form. By following the rules of algebraic simplification and practicing regularly, you can become proficient in simplifying algebraic expressions. Remember to combine like terms, remove parentheses, and rearrange the expression to make it easier to work with.

Frequently Asked Questions

Q: What is algebraic simplification?

A: Algebraic simplification is the process of reducing complex algebraic expressions to their simplest form.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms, remove parentheses, and rearrange the expression.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms.

Additional Resources

For more information on algebraic simplification, you can refer to the following resources:

• Khan Academy: Algebraic Simplification
• Mathway: Algebraic Simplification
• Wolfram Alpha: Algebraic Simplification

Final Answer

The final answer is that algebraic simplification is a crucial concept in mathematics that involves reducing complex expressions to their simplest form. By following the rules of algebraic simplification and practicing regularly, you can become proficient in simplifying algebraic expressions.