Simplify The Expression: $ 2a - {-(3b + 2a) + B} $

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. When dealing with complex expressions, it's essential to apply the correct order of operations and simplify the expression step by step. In this article, we will focus on simplifying the given expression: $ 2a - {-(3b + 2a) + b} $. We will break down the expression into manageable parts, apply the rules of arithmetic operations, and simplify it to its simplest form.

Understanding the Expression

The given expression is $ 2a - {-(3b + 2a) + b} $. To simplify this expression, we need to understand the order of operations and the rules of arithmetic. The expression contains parentheses, negations, and subtraction. We will start by simplifying the innermost parentheses and then work our way outwards.

Simplifying the Innermost Parentheses

The innermost parentheses contain the expression $ 3b + 2a $. This expression is already simplified, so we can move on to the next step.

Applying the Rules of Negation

The next step is to apply the rules of negation. When we see a negative sign in front of an expression, we can rewrite it as a positive sign and change the sign of each term inside the parentheses. In this case, we have $ -(3b + 2a) $. Applying the rules of negation, we get:

$ -(3b + 2a) = -3b - 2a $

Simplifying the Expression Inside the Curly Brackets

Now that we have simplified the expression inside the parentheses, we can move on to the expression inside the curly brackets: $ -3b - 2a + b $. We can combine like terms by adding or subtracting the coefficients of the same variable. In this case, we have:

$ -3b - 2a + b = -2b - 2a $

Simplifying the Entire Expression

Now that we have simplified the expression inside the curly brackets, we can move on to the entire expression: $ 2a - {-2b - 2a} $. We can simplify this expression by applying the rules of arithmetic operations. When we see a negative sign in front of an expression, we can rewrite it as a positive sign and change the sign of each term inside the parentheses. In this case, we have:

$ 2a - {-2b - 2a} = 2a + 2b + 2a $

Combining Like Terms

Now that we have simplified the expression, we can combine like terms by adding or subtracting the coefficients of the same variable. In this case, we have:

$ 2a + 2b + 2a = 4a + 2b $

Conclusion

In this article, we simplified the expression $ 2a - {-(3b + 2a) + b} $ step by step. We applied the rules of arithmetic operations, simplified the innermost parentheses, and combined like terms to arrive at the final simplified expression: $ 4a + 2b $. This expression is now in its simplest form, and we can use it to solve problems efficiently and accurately.

Frequently Asked Questions

  • Q: What is the order of operations in mathematics? A: The order of operations in mathematics is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS).
  • Q: How do I simplify an expression with parentheses? A: To simplify an expression with parentheses, start by simplifying the innermost parentheses and then work your way outwards.
  • Q: What is the rule for negation in mathematics? A: The rule for negation in mathematics is to change the sign of each term inside the parentheses when we see a negative sign in front of an expression.

Final Answer

The final simplified expression is $ 4a + 2b $.

Introduction

In our previous article, we simplified the expression $ 2a - {-(3b + 2a) + b} $ step by step. We applied the rules of arithmetic operations, simplified the innermost parentheses, and combined like terms to arrive at the final simplified expression: $ 4a + 2b $. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional tips and resources for further learning.

Q&A

Q: What is the order of operations in mathematics?

A: The order of operations in mathematics is Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (PEMDAS). This means that we should perform operations inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, start by simplifying the innermost parentheses and then work your way outwards. This will help you avoid confusion and ensure that you are performing the correct operations.

Q: What is the rule for negation in mathematics?

A: The rule for negation in mathematics is to change the sign of each term inside the parentheses when we see a negative sign in front of an expression. For example, $ -(3b + 2a) = -3b - 2a $.

Q: How do I combine like terms in an expression?

A: To combine like terms in an expression, add or subtract the coefficients of the same variable. For example, $ 2a + 2a = 4a $.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change. For example, $ x $ is a variable, while $ 5 $ is a constant.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, find the least common denominator (LCD) of the fractions and multiply each fraction by the LCD. Then, combine the fractions by adding or subtracting the numerators.

Q: What is the rule for distributing a negative sign in an expression?

A: The rule for distributing a negative sign in an expression is to change the sign of each term inside the parentheses. For example, $ -(3b + 2a) = -3b - 2a $.

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

A: To simplify an expression with absolute value, remove the absolute value sign and simplify the expression inside. For example, $ |3b + 2a| = 3b + 2a $.

Tips and Resources

  • To simplify an expression, start by simplifying the innermost parentheses and then work your way outwards.
  • Use the order of operations (PEMDAS) to ensure that you are performing the correct operations.
  • Combine like terms by adding or subtracting the coefficients of the same variable.
  • Use the rule for negation to change the sign of each term inside the parentheses when you see a negative sign in front of an expression.
  • Use the rule for distributing a negative sign to change the sign of each term inside the parentheses.
  • Use the rule for absolute value to remove the absolute value sign and simplify the expression inside.

Additional Resources

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • IXL: Simplifying Expressions

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations, simplifying the innermost parentheses, and combining like terms, we can simplify complex expressions and arrive at the final simplified expression. We hope that this article has provided you with a better understanding of how to simplify expressions and has given you the confidence to tackle more complex problems.