If M=-2and N=6then Evaluate The Expression 3m3+2m2n+n3=
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students and professionals alike. In this article, we will explore the process of evaluating algebraic expressions, using the given expression 3m^3 + 2m^2n + n^3 as an example. We will also provide a step-by-step guide on how to evaluate the expression when m = -2 and n = 6.
Understanding Algebraic Expressions
An algebraic expression is a mathematical statement that consists of variables, constants, and mathematical operations. It is a way of representing a value or a relationship between values using symbols and mathematical notation. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.
Evaluating the Expression 3m^3 + 2m^2n + n^3
To evaluate the expression 3m^3 + 2m^2n + n^3, we need to follow the order of operations (PEMDAS):
- Parentheses: There are no parentheses in the expression, so we move on to the next step.
- Exponents: We need to evaluate the exponents in the expression. In this case, we have m^3 and n^3.
- Multiplication: We need to multiply the coefficients of the terms. In this case, we have 3m^3, 2m^2n, and n^3.
- Addition: We need to add the terms together.
Substituting Values for m and n
Now that we have a good understanding of the expression, we can substitute the given values for m and n. We are given that m = -2 and n = 6.
Evaluating the Expression with m = -2 and n = 6
To evaluate the expression 3m^3 + 2m^2n + n^3 when m = -2 and n = 6, we need to substitute the values of m and n into the expression.
Step 1: Evaluate the Exponents
First, we need to evaluate the exponents in the expression. We have m^3 and n^3.
- m^3 = (-2)^3 = -8
- n^3 = 6^3 = 216
Step 2: Multiply the Coefficients
Next, we need to multiply the coefficients of the terms. We have 3m^3, 2m^2n, and n^3.
- 3m^3 = 3(-8) = -24
- 2m^2n = 2(-2)^2(6) = 2(4)(6) = 48
- n^3 = 216
Step 3: Add the Terms
Finally, we need to add the terms together.
- 3m^3 + 2m^2n + n^3 = -24 + 48 + 216
- 3m^3 + 2m^2n + n^3 = 240
Conclusion
In this article, we have evaluated the algebraic expression 3m^3 + 2m^2n + n^3 when m = -2 and n = 6. We have followed the order of operations (PEMDAS) and substituted the values of m and n into the expression. The final answer is 240.
Frequently Asked Questions
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical statement that consists of variables, constants, and mathematical operations.
Q: How do I evaluate an algebraic expression?
A: To evaluate an algebraic expression, you need to follow the order of operations (PEMDAS): parentheses, exponents, multiplication, and addition.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an algebraic expression. The acronym PEMDAS stands for:
- P: Parentheses
- E: Exponents
- M: Multiplication
- D: Division
- A: Addition
- S: Subtraction
Q: How do I substitute values into an algebraic expression?
A: To substitute values into an algebraic expression, you need to replace the variables with the given values and perform the operations.
References
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Introduction
Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students and professionals alike. In this article, we will provide answers to frequently asked questions about algebraic expressions, including how to evaluate them, the order of operations, and substituting values.
Q&A
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical statement that consists of variables, constants, and mathematical operations.
Q: How do I evaluate an algebraic expression?
A: To evaluate an algebraic expression, you need to follow the order of operations (PEMDAS): parentheses, exponents, multiplication, and addition.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an algebraic expression. The acronym PEMDAS stands for:
- P: Parentheses
- E: Exponents
- M: Multiplication
- D: Division
- A: Addition
- S: Subtraction
Q: How do I substitute values into an algebraic expression?
A: To substitute values into an algebraic expression, you need to replace the variables with the given values and perform the operations.
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 remains the same.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary operations.
Q: What is a like term?
A: A like term is a term that has the same variable and exponent.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the terms.
Q: What is the distributive property?
A: The distributive property is a rule that allows you to multiply a single term by multiple terms.
Q: How do I use the distributive property?
A: To use the distributive property, you need to multiply each term inside the parentheses by the term outside the parentheses.
Q: What is the commutative property?
A: The commutative property is a rule that allows you to change the order of the terms in an expression.
Q: How do I use the commutative property?
A: To use the commutative property, you need to change the order of the terms in the expression.
Q: What is the associative property?
A: The associative property is a rule that allows you to change the order of the terms in an expression.
Q: How do I use the associative property?
A: To use the associative property, you need to change the order of the terms in the expression.
Conclusion
In this article, we have provided answers to frequently asked questions about algebraic expressions, including how to evaluate them, the order of operations, and substituting values. We hope that this article has been helpful in clarifying any confusion and providing a better understanding of algebraic expressions.
Frequently Asked Questions (FAQs)
Q: What is the difference between an equation and an expression?
A: An equation is a statement that says two expressions are equal, while an expression is a mathematical statement that consists of variables, constants, and mathematical operations.
Q: How do I solve an equation?
A: To solve an equation, you need to isolate the variable by performing inverse operations.
Q: What is an inverse operation?
A: An inverse operation is an operation that undoes another operation.
Q: How do I use inverse operations to solve an equation?
A: To use inverse operations to solve an equation, you need to perform the inverse operation of the operation that was used to create the equation.