Simplify The Expression: ${ 3 + 3x + 7x - 6 }$
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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 focus on simplifying a specific algebraic expression, which involves combining like terms and applying basic arithmetic operations. By the end of this guide, you will be able to simplify complex algebraic expressions with ease.
The Expression to Simplify
The given expression is:
Our goal is to simplify this expression by combining like terms and applying basic arithmetic operations.
Combining Like Terms
Like terms are terms that have the same variable raised to the same power. In the given expression, we have two like terms: and . To combine these terms, we need to add their coefficients.
# Define the coefficients of the like terms
coefficient_1 = 3
coefficient_2 = 7
combined_coefficient = coefficient_1 + coefficient_2
print(f"The combined coefficient is: {combined_coefficient}x")
When we run this code, we get:
The combined coefficient is: 10x
So, the combined term is .
Simplifying the Expression
Now that we have combined the like terms, we can simplify the expression by combining the constant terms and the variable terms.
# Define the constant terms
constant_term_1 = 3
constant_term_2 = -6
simplified_constant = constant_term_1 + constant_term_2
variable_term = "10x"
simplified_expression = f"{simplified_constant} + {variable_term}"
print(f"The simplified expression is: {simplified_expression}")
When we run this code, we get:
The simplified expression is: -3 + 10x
So, the simplified expression is .
Conclusion
In this article, we simplified the given algebraic expression by combining like terms and applying basic arithmetic operations. We used Python code to demonstrate the steps involved in simplifying the expression. By following these steps, you can simplify complex algebraic expressions with ease.
Tips and Tricks
- When combining like terms, make sure to add their coefficients.
- When simplifying the expression, combine the constant terms and the variable terms separately.
- Use Python code to demonstrate the steps involved in simplifying the expression.
Frequently Asked Questions
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and arithmetic operations.
Q: What is a like term?
A: A like term is a term that has the same variable raised to the same power.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, combine like terms and apply basic arithmetic operations.
Q: What is the order of operations in algebra?
A: The order of operations in algebra is:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Further Reading
References
By following the steps outlined in this article, you can simplify complex algebraic expressions with ease. Remember to combine like terms and apply basic arithmetic operations to simplify the expression. Happy math-ing!
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Introduction
Simplifying algebraic expressions is a fundamental concept in mathematics, and it's essential to understand the steps involved in simplifying complex expressions. In this article, we will provide a comprehensive Q&A guide on algebraic expression simplification, covering various topics and scenarios.
Q&A: Algebraic Expression Simplification
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and arithmetic operations.
Q: What is a like term?
A: A like term is a term that has the same variable raised to the same power.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, combine like terms and apply basic arithmetic operations.
Q: What is the order of operations in algebra?
A: The order of operations in algebra is:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Q: How do I combine like terms?
A: To combine like terms, add their coefficients.
Q: What is a coefficient?
A: A coefficient is a number that is multiplied by a variable.
Q: How do I simplify an expression with multiple variables?
A: To simplify an expression with multiple variables, combine like terms for each variable separately.
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 remains the same.
Q: How do I simplify an expression with parentheses?
A: To simplify an expression with parentheses, evaluate the expression inside the parentheses first.
Q: What is the distributive property?
A: The distributive property is a rule that states that a single term can be distributed to multiple terms.
Q: How do I apply the distributive property?
A: To apply the distributive property, multiply the single term by each of the multiple terms.
Q: What is the commutative property?
A: The commutative property is a rule that states that the order of the terms does not change the result.
Q: How do I apply the commutative property?
A: To apply the commutative property, swap the order of the terms.
Q: What is the associative property?
A: The associative property is a rule that states that the order in which we perform operations does not change the result.
Q: How do I apply the associative property?
A: To apply the associative property, change the order in which we perform operations.
Tips and Tricks
- When combining like terms, make sure to add their coefficients.
- When simplifying the expression, combine the constant terms and the variable terms separately.
- Use the order of operations to simplify the expression.
- Apply the distributive property to simplify expressions with multiple terms.
- Use the commutative and associative properties to simplify expressions.
Frequently Asked Questions
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 remains the same.
Q: How do I simplify an expression with multiple variables?
A: To simplify an expression with multiple variables, combine like terms for each variable separately.
Q: What is the order of operations in algebra?
A: The order of operations in algebra is:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Q: How do I apply the distributive property?
A: To apply the distributive property, multiply the single term by each of the multiple terms.
Q: What is the commutative property?
A: The commutative property is a rule that states that the order of the terms does not change the result.
Q: How do I apply the commutative property?
A: To apply the commutative property, swap the order of the terms.
Q: What is the associative property?
A: The associative property is a rule that states that the order in which we perform operations does not change the result.
Q: How do I apply the associative property?
A: To apply the associative property, change the order in which we perform operations.
Further Reading
- Algebraic Expressions
- Like Terms
- Order of Operations
- Distributive Property
- Commutative Property
- Associative Property
References
By following the steps outlined in this article, you can simplify complex algebraic expressions with ease. Remember to combine like terms, apply the order of operations, and use the distributive, commutative, and associative properties to simplify expressions. Happy math-ing!