Simplify The Expression: $6(g+h$\]

Simplify the Expression: 6(g+h)

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms and removing any unnecessary components from the expression. In this article, we will simplify the expression $6(g+h)$, which is a basic algebraic expression.

Understanding the Expression

The given expression is $6(g+h)$. This expression consists of two terms: $g$ and $h$. The term $g$ is a variable, and the term $h$ is also a variable. The expression is multiplied by 6, which is a constant.

Simplifying the Expression

To simplify the expression, we need to apply the distributive property of multiplication over addition. The distributive property states that for any numbers $a$, $b$, and $c$, the following equation holds:

$a(b+c) = ab + ac$

Using this property, we can simplify the expression $6(g+h)$ as follows:

$6(g+h) = 6g + 6h$

Step-by-Step Solution

Here's a step-by-step solution to simplify the expression:

1. Apply the distributive property: We apply the distributive property to the expression $6(g+h)$.
2. Distribute the 6: We distribute the 6 to both terms inside the parentheses, $g$ and $h$.
3. Combine like terms: We combine the like terms $6g$ and $6h$ to get the final simplified expression.

Final Answer

The final simplified expression is $6g + 6h$.

Example Use Case

Simplifying expressions like $6(g+h)$ is essential in algebra and mathematics. For example, consider the equation:

$2x + 3y = 12$

We can simplify this equation by combining like terms:

$2x + 3y = 12$

$2x + 3y - 2x = 12 - 2x$

$3y = 12 - 2x$

$y = \frac{12 - 2x}{3}$

In this example, we simplified the equation by combining like terms and removing unnecessary components.

Conclusion

Simplifying expressions like $6(g+h)$ is a fundamental skill in algebra and mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and solve equations and inequalities. In this article, we simplified the expression $6(g+h)$ and provided a step-by-step solution to demonstrate the process.

Common Mistakes to Avoid

When simplifying expressions, it's essential to avoid common mistakes like:

• Not applying the distributive property: Failing to apply the distributive property can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can result in complex and unnecessary expressions.
• Not removing unnecessary components: Failing to remove unnecessary components can lead to incorrect solutions.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions like $6(g+h)$:

• Use the distributive property: Apply the distributive property to simplify expressions.
• Combine like terms: Combine like terms to simplify expressions.
• Remove unnecessary components: Remove unnecessary components to simplify expressions.
• Check your work: Check your work to ensure that the simplified expression is correct.

Practice Problems

Here are some practice problems to help you simplify expressions like $6(g+h)$:

• Simplify the expression: $3(x+y)$
• Simplify the expression: $2(a+b)$
• Simplify the expression: $4(c+d)$

Conclusion

Simplifying expressions like $6(g+h)$ is a fundamental skill in algebra and mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and solve equations and inequalities. In this article, we simplified the expression $6(g+h)$ and provided a step-by-step solution to demonstrate the process.
Simplify the Expression: 6(g+h) - Q&A

In our previous article, we simplified the expression $6(g+h)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions like $6(g+h)$.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any numbers $a$, $b$, and $c$, the following equation holds:

$a(b+c) = ab + ac$

This property allows us to distribute a single term to multiple terms inside parentheses.

Q: How do I simplify expressions like $6(g+h)$?

A: To simplify expressions like $6(g+h)$, you need to apply the distributive property and combine like terms. Here's a step-by-step solution:

1. Apply the distributive property: Apply the distributive property to the expression $6(g+h)$.
2. Distribute the 6: Distribute the 6 to both terms inside the parentheses, $g$ and $h$.
3. Combine like terms: Combine the like terms $6g$ and $6h$ to get the final simplified expression.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. For example, $2x$ and $3x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the expression $2x + 3x$, you can combine the like terms by adding the coefficients:

$2x + 3x = (2+3)x = 5x$

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not applying the distributive property: Failing to apply the distributive property can lead to incorrect simplifications.
• Not combining like terms: Failing to combine like terms can result in complex and unnecessary expressions.
• Not removing unnecessary components: Failing to remove unnecessary components can lead to incorrect solutions.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, you need to:

• Re-read the original expression: Re-read the original expression to ensure that you understand what you are simplifying.
• Apply the distributive property: Apply the distributive property to the expression.
• Combine like terms: Combine like terms to simplify the expression.
• Check the final answer: Check the final answer to ensure that it is correct.

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions has many real-world applications, including:

• Algebra: Simplifying expressions is a fundamental skill in algebra, which is used to solve equations and inequalities.
• Calculus: Simplifying expressions is used in calculus to find derivatives and integrals.
• Physics: Simplifying expressions is used in physics to solve problems related to motion, energy, and momentum.

Conclusion

Simplifying expressions like $6(g+h)$ is a fundamental skill in algebra and mathematics. By applying the distributive property and combining like terms, we can simplify complex expressions and solve equations and inequalities. In this article, we answered some frequently asked questions (FAQs) related to simplifying expressions like $6(g+h)$.