Simplify The Expression: $ 4[-3x(x+3)] $
Introduction
In mathematics, simplifying expressions is a crucial skill that helps us solve problems more efficiently. It involves rewriting an expression in a simpler form, often by combining like terms or removing unnecessary brackets. In this article, we will focus on simplifying the expression $ 4[-3x(x+3)] $, which involves applying the distributive property and combining like terms.
Understanding the Expression
The given expression is $ 4[-3x(x+3)] $. To simplify this expression, we need to understand the order of operations and the properties of exponents. The expression involves a negative sign, which indicates that we need to multiply the terms inside the brackets by -1.
Applying the Distributive Property
The distributive property states that for any real numbers a, b, and c, the following equation holds:
a(b + c) = ab + ac
We can apply this property to the expression $ -3x(x+3) $ by distributing the -3x to the terms inside the brackets.
Step 1: Distribute -3x to the terms inside the brackets
$ -3x(x+3) = -3x \cdot x + (-3x) \cdot 3 $
Step 2: Simplify the expression
$ -3x \cdot x + (-3x) \cdot 3 = -3x^2 - 9x $
Step 3: Multiply the expression by 4
$ 4(-3x^2 - 9x) = -12x^2 - 36x $
Conclusion
By applying the distributive property and combining like terms, we have simplified the expression $ 4[-3x(x+3)] $ to $ -12x^2 - 36x $. This simplified expression is easier to work with and can be used to solve problems involving quadratic equations.
Tips and Tricks
- When simplifying expressions, always follow the order of operations (PEMDAS).
- Use the distributive property to expand expressions with brackets.
- Combine like terms to simplify the expression.
- Check your work by plugging in values or using a calculator.
Real-World Applications
Simplifying expressions is an essential skill in mathematics, and it has many real-world applications. For example, in physics, simplifying expressions can help us solve problems involving motion and energy. In engineering, simplifying expressions can help us design and optimize systems.
Common Mistakes
- Failing to apply the distributive property when expanding expressions with brackets.
- Not combining like terms when simplifying expressions.
- Not following the order of operations (PEMDAS).
Conclusion
Simplifying expressions is a crucial skill in mathematics that helps us solve problems more efficiently. By applying the distributive property and combining like terms, we can simplify expressions and make them easier to work with. Remember to follow the order of operations (PEMDAS) and check your work by plugging in values or using a calculator.
Final Answer
The final answer is: $ -12x^2 - 36x $
Frequently Asked Questions
- Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac.
- Q: How do I simplify expressions? A: To simplify expressions, follow the order of operations (PEMDAS) and apply the distributive property to expand expressions with brackets. Then, combine like terms to simplify the expression.
- Q: What are like terms?
A: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms because they both have the variable x and the exponent 1.
Introduction
In our previous article, we simplified the expression $ 4[-3x(x+3)] $ to $ -12x^2 - 36x $. However, we received many questions from readers who were struggling to understand the concept of simplifying expressions. In this article, we will address some of the most frequently asked questions and provide additional explanations to help you master the art of simplifying expressions.
Q&A
Q: What is the distributive property?
A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, the following equation holds:
a(b + c) = ab + ac
This property allows us to expand expressions with brackets by multiplying the terms inside the brackets by the factor outside the brackets.
Q: How do I simplify expressions?
A: To simplify expressions, follow the order of operations (PEMDAS) and apply the distributive property to expand expressions with brackets. Then, combine like terms to simplify the expression.
Q: What are like terms?
A: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms because they both have the variable x and the exponent 1.
Q: How do I combine like terms?
A: To combine like terms, add or subtract the coefficients of the like terms. For example, 2x + 3x = 5x.
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 expressions. The acronym PEMDAS stands for:
- 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 expressions with negative signs?
A: When simplifying expressions with negative signs, remember that a negative sign outside the brackets means that you need to multiply the terms inside the brackets by -1.
Q: Can you provide more examples of simplifying expressions?
A: Here are a few more examples:
- Simplify the expression: $ 2(x + 3) $
- Simplify the expression: $ 3(x - 2) $
- Simplify the expression: $ 4(x + 2) - 2(x - 3) $
Q: How do I know when to use the distributive property?
A: You should use the distributive property when you have an expression with a bracket and a factor outside the bracket. For example, in the expression $ 2(x + 3) $, you would use the distributive property to expand the expression to $ 2x + 6 $.
Tips and Tricks
- Always follow the order of operations (PEMDAS) when simplifying expressions.
- Use the distributive property to expand expressions with brackets.
- Combine like terms to simplify the expression.
- Check your work by plugging in values or using a calculator.
Real-World Applications
Simplifying expressions is an essential skill in mathematics, and it has many real-world applications. For example, in physics, simplifying expressions can help us solve problems involving motion and energy. In engineering, simplifying expressions can help us design and optimize systems.
Common Mistakes
- Failing to apply the distributive property when expanding expressions with brackets.
- Not combining like terms when simplifying expressions.
- Not following the order of operations (PEMDAS).
Conclusion
Simplifying expressions is a crucial skill in mathematics that helps us solve problems more efficiently. By following the order of operations (PEMDAS) and applying the distributive property, we can simplify expressions and make them easier to work with. Remember to combine like terms and check your work by plugging in values or using a calculator.
Final Answer
The final answer is: $ -12x^2 - 36x $
Frequently Asked Questions
- Q: What is the distributive property? A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac.
- Q: How do I simplify expressions? A: To simplify expressions, follow the order of operations (PEMDAS) and apply the distributive property to expand expressions with brackets. Then, combine like terms to simplify the expression.
- Q: What are like terms? A: Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms because they both have the variable x and the exponent 1.