Simplify The Expression:$(2h + 3)(3h - 2$\]
Simplify the Expression: (2h + 3)(3h - 2)
In algebra, simplifying expressions is a crucial skill that helps us solve equations and manipulate mathematical statements. One of the most common techniques used to simplify expressions is the distributive property, which allows us to expand and combine like terms. In this article, we will use the distributive property to simplify the expression (2h + 3)(3h - 2).
Understanding the Distributive Property
The distributive property is a fundamental concept in algebra that states:
a(b + c) = ab + ac
This property allows us to distribute a single term to multiple terms inside a set of parentheses. In the context of the given expression, we can use the distributive property to expand and simplify the product of two binomials.
Simplifying the Expression
To simplify the expression (2h + 3)(3h - 2), we will use the distributive property to expand and combine like terms. We will start by multiplying each term in the first binomial (2h + 3) with each term in the second binomial (3h - 2).
Step 1: Multiply the First Term in the First Binomial with Each Term in the Second Binomial
We will start by multiplying the first term in the first binomial (2h) with each term in the second binomial (3h - 2).
2h(3h) = 6h^2
2h(-2) = -4h
Step 2: Multiply the Second Term in the First Binomial with Each Term in the Second Binomial
Next, we will multiply the second term in the first binomial (3) with each term in the second binomial (3h - 2).
3(3h) = 9h
3(-2) = -6
Step 3: Combine Like Terms
Now that we have expanded and simplified the product of the two binomials, we can combine like terms to get the final simplified expression.
6h^2 - 4h + 9h - 6
We can combine the like terms -4h and 9h to get 5h.
The final simplified expression is:
6h^2 + 5h - 6
In this article, we used the distributive property to simplify the expression (2h + 3)(3h - 2). We expanded and combined like terms to get the final simplified expression. The distributive property is a powerful tool in algebra that allows us to manipulate and simplify complex expressions. By understanding and applying this property, we can solve equations and manipulate mathematical statements with ease.
- When simplifying expressions, always use the distributive property to expand and combine like terms.
- Make sure to combine like terms carefully to avoid errors.
- Use the distributive property to simplify complex expressions and equations.
- Failing to use the distributive property when simplifying expressions.
- Not combining like terms carefully.
- Making errors when multiplying and combining terms.
The distributive property has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, the distributive property is used to calculate the force and momentum of objects. In engineering, the distributive property is used to design and optimize complex systems. In economics, the distributive property is used to analyze and model economic systems.
In our previous article, we used the distributive property to simplify the expression (2h + 3)(3h - 2). We expanded and combined like terms to get the final simplified expression. In this article, we will answer some frequently asked questions about simplifying expressions and the distributive property.
Q: What is the distributive property?
A: The distributive property is a fundamental concept in algebra that states:
a(b + c) = ab + ac
This property allows us to distribute a single term to multiple terms inside a set of parentheses.
Q: How do I use the distributive property to simplify expressions?
A: To use the distributive property to simplify expressions, follow these steps:
- Multiply each term in the first binomial with each term in the second binomial.
- Combine like terms to get the final simplified expression.
Q: What are like terms?
A: Like terms are terms that have the same variable and exponent. For example, 2h and 4h are like terms because they both have the variable h 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, 2h + 4h = 6h.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Failing to use the distributive property when simplifying expressions.
- Not combining like terms carefully.
- Making errors when multiplying and combining terms.
Q: How do I apply the distributive property to real-world problems?
A: The distributive property has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, the distributive property is used to calculate the force and momentum of objects. In engineering, the distributive property is used to design and optimize complex systems. In economics, the distributive property is used to analyze and model economic systems.
Q: What are some tips and tricks for simplifying expressions?
A: Some tips and tricks for simplifying expressions include:
- Using the distributive property to simplify complex expressions and equations.
- Combining like terms carefully to avoid errors.
- Making sure to multiply and combine terms correctly.
Q: How do I practice simplifying expressions?
A: To practice simplifying expressions, try the following:
- Start with simple expressions and gradually move on to more complex ones.
- Use online resources and practice problems to help you practice simplifying expressions.
- Work with a partner or tutor to help you understand and apply the distributive property.
In this article, we answered some frequently asked questions about simplifying expressions and the distributive property. We covered topics such as the distributive property, like terms, combining like terms, and common mistakes to avoid. We also provided tips and tricks for simplifying expressions and practicing with real-world problems. By understanding and applying the distributive property, you can simplify complex expressions and equations with ease.
Simplifying expressions is a crucial skill in algebra that helps us solve equations and manipulate mathematical statements. The distributive property is a powerful tool that allows us to expand and combine like terms. By understanding and applying this property, we can simplify complex expressions and equations with ease. Remember to use the distributive property to simplify expressions, combine like terms carefully, and avoid common mistakes. With practice and patience, you will become proficient in simplifying expressions and solving equations.