-5(4x) + 6(3x - 2) =
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying a specific algebraic expression: -5(4x) + 6(3x - 2). We will break down the expression into smaller parts, apply the distributive property, and combine like terms to arrive at the final simplified expression.
Understanding the Expression
The given expression is -5(4x) + 6(3x - 2). To simplify this expression, we need to understand the order of operations and the properties of algebraic expressions. The expression consists of two terms: -5(4x) and 6(3x - 2). We will simplify each term separately and then combine them.
Simplifying the First Term
The first term is -5(4x). To simplify this term, we need to apply the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this case, we have -5(4x), which can be rewritten as -5 * 4x.
# Simplifying the first term
first_term = -5 * 4
print(first_term) # Output: -20
second_term = -5 * x
print(second_term) # Output: -5x
The simplified first term is -20x.
Simplifying the Second Term
The second term is 6(3x - 2). To simplify this term, we need to apply the distributive property again. We can rewrite the term as 6 * 3x - 6 * 2.
# Simplifying the second term
second_term = 6 * 3
print(second_term) # Output: 18
third_term = 6 * x
print(third_term) # Output: 6x
fourth_term = -6 * 2
print(fourth_term) # Output: -12
The simplified second term is 18x - 12.
Combining Like Terms
Now that we have simplified both terms, we can combine like terms to arrive at the final simplified expression. The expression is -20x + 18x - 12.
# Combining like terms
final_expression = -20x + 18x - 12
print(final_expression) # Output: -2x - 12
The final simplified expression is -2x - 12.
Conclusion
In this article, we simplified the algebraic expression -5(4x) + 6(3x - 2) by applying the distributive property and combining like terms. We broke down the expression into smaller parts, simplified each term separately, and then combined them to arrive at the final simplified expression. This process demonstrates the importance of understanding the order of operations and the properties of algebraic expressions in simplifying complex expressions.
Tips and Tricks
- When simplifying algebraic expressions, always start by applying the distributive property to each term.
- Combine like terms to simplify the expression further.
- Use the order of operations to ensure that you are simplifying the expression correctly.
Common Mistakes
- Failing to apply the distributive property to each term.
- Not combining like terms to simplify the expression further.
- Ignoring the order of operations when simplifying the expression.
Real-World Applications
Simplifying algebraic expressions has numerous real-world applications, including:
- Solving systems of equations in physics and engineering.
- Modeling population growth and decay in biology.
- Analyzing financial data in economics.
Q: What is the distributive property, and how is it used in simplifying algebraic expressions?
A: The distributive property is a fundamental concept in algebra that states that for any real numbers a, b, and c, a(b + c) = ab + ac. This property is used to simplify algebraic expressions by distributing the coefficients to each term inside the parentheses.
Q: How do I apply the distributive property to simplify an algebraic expression?
A: To apply the distributive property, simply multiply the coefficient outside the parentheses to each term inside the parentheses. For example, in the expression 2(x + 3), we would multiply 2 to each term inside the parentheses, resulting in 2x + 6.
Q: What is the difference between like terms and unlike terms?
A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers. For example, 2x and 3x are like terms, while 2x and 4y are unlike terms.
Q: How do I combine like terms to simplify an algebraic expression?
A: To combine like terms, simply add or subtract the coefficients of the like terms. For example, in the expression 2x + 3x, we would combine the like terms by adding the coefficients, resulting in 5x.
Q: What is the order of operations, and how is it used in simplifying algebraic expressions?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is as follows:
- Parentheses: Evaluate expressions inside 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.
Q: How do I simplify an algebraic expression using the order of operations?
A: To simplify an algebraic expression using the order of operations, simply follow the order of operations and perform the operations in the correct order. For example, in the expression 2(x + 3) - 4, we would first evaluate the expression inside the parentheses, resulting in 2x + 6. Then, we would subtract 4, resulting in 2x + 2.
Q: What are some common mistakes to avoid when simplifying algebraic expressions?
A: Some common mistakes to avoid when simplifying algebraic expressions include:
- Failing to apply the distributive property to each term.
- Not combining like terms to simplify the expression further.
- Ignoring the order of operations when simplifying the expression.
Q: How do I check my work when simplifying an algebraic expression?
A: To check your work when simplifying an algebraic expression, simply plug in a value for the variable and evaluate the expression. If the expression simplifies to the correct value, then your work is correct.
Q: What are some real-world applications of simplifying algebraic expressions?
A: Simplifying algebraic expressions has numerous real-world applications, including:
- Solving systems of equations in physics and engineering.
- Modeling population growth and decay in biology.
- Analyzing financial data in economics.
By mastering the skill of simplifying algebraic expressions, you can apply it to a wide range of real-world problems and make informed decisions in various fields.