Which Expression Is Equivalent To $(8a - 3b + 7) - (2a + B - 4)$?A. 6 A − 2 B + 11 6a - 2b + 11 6 A − 2 B + 11 B. 6 A − 4 B + 3 6a - 4b + 3 6 A − 4 B + 3 C. 6 A − 2 B + 3 6a - 2b + 3 6 A − 2 B + 3 D. 6 A − 4 B + 11 6a - 4b + 11 6 A − 4 B + 11

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, with a focus on the given expression: $(8a - 3b + 7) - (2a + b - 4)$. We will break down the expression into manageable parts, apply the rules of algebra, and arrive at the simplified form.

Understanding the Expression

The given expression is a combination of two algebraic expressions, each enclosed in parentheses. The first expression is 8a−3b+78a - 3b + 7, and the second expression is 2a+b−42a + b - 4. To simplify the given expression, we need to apply the rules of algebra, specifically the distributive property and the order of operations.

Applying the Distributive Property

The distributive property states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac. We can apply this property to the given expression by distributing the negative sign to each term inside the second parentheses.

(8a−3b+7)−(2a+b−4)(8a - 3b + 7) - (2a + b - 4)

Using the distributive property, we can rewrite the expression as:

8a−3b+7−2a−b+48a - 3b + 7 - 2a - b + 4

Combining Like Terms

Now that we have distributed the negative sign, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable aa, and two terms with the variable bb.

8a−2a−3b−b+7+48a - 2a - 3b - b + 7 + 4

Combining like terms, we get:

6a−4b+116a - 4b + 11

Conclusion

In conclusion, the simplified form of the given expression is 6a−4b+116a - 4b + 11. This expression is equivalent to the original expression, and it is the correct answer among the options provided.

Answer Key

The correct answer is:

  • D. 6a−4b+116a - 4b + 11

Tips and Tricks

When simplifying algebraic expressions, it's essential to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate 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.

By following the order of operations and applying the rules of algebra, you can simplify even the most complex algebraic expressions.

Common Mistakes

When simplifying algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Forgetting to distribute the negative sign: When simplifying expressions with negative signs, make sure to distribute the negative sign to each term inside the parentheses.
  • Not combining like terms: When combining like terms, make sure to add or subtract the coefficients of the terms with the same variable raised to the same power.
  • Not following the order of operations: When simplifying expressions, make sure to follow the order of operations (PEMDAS) to ensure that you evaluate the expressions in the correct order.

Practice Problems

To practice simplifying algebraic expressions, try the following problems:

  • Simplify the expression: $(3x + 2y - 4) - (2x - y + 3)$
  • Simplify the expression: $(2a - 3b + 5) + (a + 2b - 2)$
  • Simplify the expression: $(4x + 2y - 3) - (2x - y + 1)$

By practicing these problems, you can improve your skills in simplifying algebraic expressions and become more confident in your math abilities.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By following the rules of algebra, applying the distributive property, and combining like terms, you can simplify even the most complex expressions. Remember to follow the order of operations (PEMDAS) and avoid common mistakes to ensure that you arrive at the correct answer. With practice and patience, you can become proficient in simplifying algebraic expressions and tackle even the most challenging math problems.

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Introduction

In our previous article, we explored the process of simplifying algebraic expressions, with a focus on the given expression: $(8a - 3b + 7) - (2a + b - 4)$. We broke down the expression into manageable parts, applied the rules of algebra, and arrived at the simplified form. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a rule in algebra that states that for any real numbers aa, bb, and cc, a(b+c)=ab+aca(b + c) = ab + ac. This property allows us to distribute a single term to multiple terms inside parentheses.

Q: How do I simplify an expression with multiple parentheses?

A: To simplify an expression with multiple parentheses, follow these steps:

  1. Distribute the negative sign to each term inside the second parentheses.
  2. Combine like terms.
  3. Follow the order of operations (PEMDAS).

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x2x and 4x4x are like terms because they both have the variable xx raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms with the same variable raised to the same power. For example, 2x+4x=6x2x + 4x = 6x.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

  1. Parentheses: Evaluate 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: How do I avoid common mistakes when simplifying algebraic expressions?

A: To avoid common mistakes when simplifying algebraic expressions, follow these tips:

  • Make sure to distribute the negative sign to each term inside the parentheses.
  • Combine like terms carefully.
  • Follow the order of operations (PEMDAS) to ensure that you evaluate the expressions in the correct order.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By following the rules of algebra, applying the distributive property, and combining like terms, you can simplify even the most complex expressions. Remember to follow the order of operations (PEMDAS) and avoid common mistakes to ensure that you arrive at the correct answer. With practice and patience, you can become proficient in simplifying algebraic expressions and tackle even the most challenging math problems.

Practice Problems

To practice simplifying algebraic expressions, try the following problems:

  • Simplify the expression: $(3x + 2y - 4) - (2x - y + 3)$
  • Simplify the expression: $(2a - 3b + 5) + (a + 2b - 2)$
  • Simplify the expression: $(4x + 2y - 3) - (2x - y + 1)$

By practicing these problems, you can improve your skills in simplifying algebraic expressions and become more confident in your math abilities.

Additional Resources

For more information on simplifying algebraic expressions, check out the following resources:

  • Khan Academy: Algebraic Expressions
  • Mathway: Simplifying Algebraic Expressions
  • Wolfram Alpha: Algebraic Expressions

By following these resources and practicing regularly, you can become proficient in simplifying algebraic expressions and tackle even the most challenging math problems.