Simplify The Expression. First, Use The Distributive Property.${ 3 + 5(w + 3) + W }$ { 3 + 5(w + 3) + W = \square \}

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. One of the most powerful tools for simplifying expressions is the distributive property. In this article, we will use the distributive property to simplify the given expression: $3 + 5(w + 3) + w$. We will break down the steps and provide a clear explanation of each step.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses. The distributive property can be written as:

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

where $a$, $b$, and $c$ are variables or constants.

Step 1: Apply the Distributive Property

To simplify the given expression, we will apply the distributive property to the term $5(w + 3)$. We will multiply each term inside the parentheses by the term outside the parentheses, which is $5$.

$5(w + 3) = 5w + 15$

Now, we can rewrite the original expression as:

$3 + 5w + 15 + w$

Step 2: Combine Like Terms

The next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable $w$: $5w$ and $w$. We can combine these terms by adding their coefficients.

$5w + w = 6w$

Now, we can rewrite the expression as:

$3 + 15 + 6w$

Step 3: Simplify the Constants

The final step is to simplify the constants. We can add the constants $3$ and $15$ to get:

$18 + 6w$

Conclusion

In this article, we used the distributive property to simplify the given expression: $3 + 5(w + 3) + w$. We broke down the steps and provided a clear explanation of each step. By applying the distributive property and combining like terms, we were able to simplify the expression to $18 + 6w$. This is a powerful example of how the distributive property can be used to simplify expressions and solve equations.

Example Problems

Here are a few example problems that demonstrate the use of the distributive property:

• $2(x + 4) = \square$
• $3(2y + 1) = \square$
• $4(a + 2) = \square$

Solutions

• $2(x + 4) = 2x + 8$
• $3(2y + 1) = 6y + 3$
• $4(a + 2) = 4a + 8$

Tips and Tricks

Here are a few tips and tricks to help you simplify expressions using the distributive property:

• Make sure to apply the distributive property to each term inside the parentheses.
• Combine like terms by adding their coefficients.
• Simplify the constants by adding or subtracting them.

By following these tips and tricks, you can become proficient in simplifying expressions using the distributive property.

Common Mistakes

Here are a few common mistakes to avoid when simplifying expressions using the distributive property:

• Failing to apply the distributive property to each term inside the parentheses.
• Not combining like terms.
• Not simplifying the constants.

By avoiding these common mistakes, you can ensure that your simplifications are accurate and correct.

Conclusion

Introduction

In our previous article, we used the distributive property to simplify the expression: $3 + 5(w + 3) + w$. We broke down the steps and provided a clear explanation of each step. In this article, we will answer some frequently asked questions about simplifying expressions using the distributive property.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses by the term outside the parentheses. For example, if you have the expression $a(b + c)$, you would multiply $a$ by $b$ and $c$ to get $ab + ac$.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $5x$ 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 their coefficients. For example, if you have the expression $2x + 5x$, you would add the coefficients 2 and 5 to get $7x$.

Q: What are some common mistakes to avoid when simplifying expressions using the distributive property?

A: Some common mistakes to avoid when simplifying expressions using the distributive property include:

• Failing to apply the distributive property to each term inside the parentheses.
• Not combining like terms.
• Not simplifying the constants.

Q: How do I simplify expressions with multiple variables?

A: To simplify expressions with multiple variables, you need to apply the distributive property to each term inside the parentheses and then combine like terms. For example, if you have the expression $2(x + y + z)$, you would multiply 2 by each term inside the parentheses to get $2x + 2y + 2z$.

Q: Can I use the distributive property to simplify expressions with fractions?

A: Yes, you can use the distributive property to simplify expressions with fractions. For example, if you have the expression $\frac{1}{2}(x + y)$, you would multiply $\frac{1}{2}$ by each term inside the parentheses to get $\frac{1}{2}x + \frac{1}{2}y$.

Q: How do I check my work when simplifying expressions using the distributive property?

A: To check your work when simplifying expressions using the distributive property, you need to make sure that you have applied the distributive property to each term inside the parentheses and combined like terms correctly. You can also use a calculator or a computer algebra system to check your work.

Example Problems

Here are a few example problems that demonstrate the use of the distributive property:

• $2(x + 4) = \square$
• $3(2y + 1) = \square$
• $4(a + 2) = \square$

Solutions

• $2(x + 4) = 2x + 8$
• $3(2y + 1) = 6y + 3$
• $4(a + 2) = 4a + 8$

Tips and Tricks

Here are a few tips and tricks to help you simplify expressions using the distributive property:

• Make sure to apply the distributive property to each term inside the parentheses.
• Combine like terms by adding their coefficients.
• Simplify the constants by adding or subtracting them.

By following these tips and tricks, you can become proficient in simplifying expressions using the distributive property.

Common Mistakes

Here are a few common mistakes to avoid when simplifying expressions using the distributive property:

• Failing to apply the distributive property to each term inside the parentheses.
• Not combining like terms.
• Not simplifying the constants.

By avoiding these common mistakes, you can ensure that your simplifications are accurate and correct.

Conclusion

In conclusion, the distributive property is a powerful tool for simplifying expressions. By applying the distributive property and combining like terms, we can simplify expressions and solve equations. Remember to make sure to apply the distributive property to each term inside the parentheses, combine like terms, and simplify the constants. With practice and patience, you can become proficient in simplifying expressions using the distributive property.