Select The Correct Answer. Simplify The Following Expression: { (38x + 61y) - (3x - 11y)$}$A. ${ 41x - 72y\$} B. ${ 35z + 72y\$} C. ${ 41x + 50y\$} D. ${ 35x - 50y\$}
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression using basic algebraic rules. We will break down the expression into smaller parts, apply the rules, and finally arrive at the simplified form.
The Expression to Simplify
The given expression is:
{(38x + 61y) - (3x - 11y)$}$
Our goal is to simplify this expression by combining like terms and applying basic algebraic rules.
Step 1: Distribute the Negative Sign
The first step in simplifying the expression is to distribute the negative sign to the terms inside the second set of parentheses. This will change the sign of each term inside the parentheses.
{(38x + 61y) - (3x - 11y) = 38x + 61y - 3x + 11y$}$
Step 2: Combine 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 x and two terms with the variable y.
${38x - 3x + 61y + 11y\$}
Step 3: Simplify the Terms
We can simplify the terms by combining the coefficients of the like terms. The coefficient of a term is the number that is multiplied by the variable.
{(38x - 3x) + (61y + 11y) = 35x + 72y$}$
Conclusion
We have successfully simplified the given algebraic expression using basic algebraic rules. The simplified expression is:
${35x + 72y\$}
This is the correct answer among the given options.
Comparison with Options
Let's compare our simplified expression with the given options:
- Option A: ${41x - 72y\$}
- Option B: ${35z + 72y\$}
- Option C: ${41x + 50y\$}
- Option D: ${35x - 50y\$}
Our simplified expression matches with Option A, but the signs of the terms are different. However, we can see that the correct option is not among the given choices.
Final Answer
The correct answer is not among the given options. However, we have successfully simplified the given algebraic expression using basic algebraic rules.
Frequently Asked Questions
Q: What is the correct answer?
A: The correct answer is not among the given options.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, you need to combine like terms and apply basic algebraic rules.
Q: What are like terms?
A: Like terms are terms that have the same variable 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.
Conclusion
Simplifying algebraic expressions is an essential skill for students and professionals alike. In this article, we have focused on simplifying a specific algebraic expression using basic algebraic rules. We have broken down the expression into smaller parts, applied the rules, and finally arrived at the simplified form. We have also compared our simplified expression with the given options and concluded that the correct answer is not among the given choices.
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Introduction
Simplifying algebraic expressions is a fundamental concept in mathematics, and it's essential to understand the rules and techniques involved. In our previous article, we simplified a specific algebraic expression using basic algebraic rules. In this article, we will provide a Q&A guide to help you understand the concepts and techniques involved in simplifying algebraic expressions.
Q&A Guide
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
Q: What are like terms?
A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x 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 2x + 4x, you can combine the like terms by adding the coefficients: 2x + 4x = 6x.
Q: What is the distributive property?
A: The distributive property is a rule that allows you to distribute a coefficient to multiple terms. For example, if you have 2(x + 3), you can distribute the coefficient 2 to the terms inside the parentheses: 2x + 6.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, you need to combine like terms and apply basic algebraic rules. You can also use the distributive property to simplify expressions.
Q: What are some common algebraic expressions?
A: Some common algebraic expressions include:
- Linear expressions: ax + b
- Quadratic expressions: ax^2 + bx + c
- Polynomial expressions: a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0
Q: How do I simplify a quadratic expression?
A: To simplify a quadratic expression, you need to combine like terms and apply basic algebraic rules. You can also use the distributive property to simplify expressions.
Q: What is the difference between a variable and a constant?
A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.
Q: How do I simplify an expression with parentheses?
A: To simplify an expression with parentheses, you need to follow the order of operations (PEMDAS):
- Parentheses: Evaluate the expressions inside the parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Conclusion
Simplifying algebraic expressions is an essential skill for students and professionals alike. In this article, we have provided a Q&A guide to help you understand the concepts and techniques involved in simplifying algebraic expressions. We have covered topics such as like terms, the distributive property, and simplifying quadratic expressions. By following the rules and techniques outlined in this article, you will be able to simplify algebraic expressions with ease.
Frequently Asked Questions
Q: What is the best way to simplify an algebraic expression?
A: The best way to simplify an algebraic expression is to combine like terms and apply basic algebraic rules.
Q: How do I know if an expression is simplified?
A: An expression is simplified if there are no like terms that can be combined.
Q: Can I simplify an expression with variables?
A: Yes, you can simplify an expression with variables by combining like terms and applying basic algebraic rules.
Q: How do I simplify an expression with fractions?
A: To simplify an expression with fractions, you need to combine like terms and apply basic algebraic rules.
Conclusion
Simplifying algebraic expressions is an essential skill for students and professionals alike. By following the rules and techniques outlined in this article, you will be able to simplify algebraic expressions with ease. Remember to combine like terms, apply basic algebraic rules, and follow the order of operations to simplify expressions.