Multiply. 7 ( Q + 3 7(q+3 7 ( Q + 3 ] 7 ( Q + 3 ) = 7(q+3) = 7 ( Q + 3 ) =

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Introduction

In algebra, multiplying expressions is a fundamental operation that helps us simplify complex equations and solve problems. In this article, we will focus on multiplying a single term, $7$, by a binomial expression, $(q+3)$. We will break down the process into manageable steps and provide a clear explanation of each step.

Understanding the Problem

The problem asks us to multiply $7$ by $(q+3)$. To do this, 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 $7(q+3)$, and we need to multiply $7$ by each term inside the parentheses.

Step 1: Multiply $7$ by the First Term

The first term inside the parentheses is $q$. To multiply $7$ by $q$, we simply multiply the two numbers together. This gives us $7q$.

Step 2: Multiply $7$ by the Second Term

The second term inside the parentheses is $3$. To multiply $7$ by $3$, we simply multiply the two numbers together. This gives us $21$.

Step 3: Combine the Results

Now that we have multiplied $7$ by each term inside the parentheses, we can combine the results. We have $7q$ and $21$, and we can write the final result as $7q + 21$.

Conclusion

In this article, we have learned how to multiply a single term by a binomial expression using the distributive property. We have broken down the process into manageable steps and provided a clear explanation of each step. By following these steps, we can simplify complex expressions and solve problems in algebra.

Example Problems

To reinforce our understanding of multiplying expressions, let's try some example problems.

Example 1: Multiply $5$ by $(x+2)$

Using the distributive property, we can multiply $5$ by each term inside the parentheses:

$5(x+2) = 5x + 10$

Example 2: Multiply $3$ by $(y-4)$

Using the distributive property, we can multiply $3$ by each term inside the parentheses:

$3(y-4) = 3y - 12$

Example 3: Multiply $2$ by $(z+1)$

Using the distributive property, we can multiply $2$ by each term inside the parentheses:

$2(z+1) = 2z + 2$

Tips and Tricks

When multiplying expressions, it's essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these steps and using the distributive property, we can simplify complex expressions and solve problems in algebra.

Common Mistakes to Avoid

When multiplying expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Forgetting to distribute: Make sure to multiply each term inside the parentheses by the single term outside the parentheses.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
• Not combining like terms: Make sure to combine like terms when simplifying expressions.

By avoiding these common mistakes, we can ensure that our answers are accurate and complete.

Conclusion

Introduction

In our previous article, we learned how to multiply a single term by a binomial expression using the distributive property. In this article, we will answer some common questions that students often have when multiplying expressions.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to multiply a single term by a binomial expression. It states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$.

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 single term outside the parentheses. For example, if you have $7(q+3)$, you would multiply $7$ by $q$ and $7$ by $3$.

Q: What is the difference between multiplying expressions and multiplying numbers?

A: When multiplying expressions, you need to apply the distributive property and multiply each term inside the parentheses by the single term outside the parentheses. When multiplying numbers, you simply multiply the two numbers together.

Q: Can I multiply expressions with more than two terms?

A: Yes, you can multiply expressions with more than two terms. For example, if you have $7(q+3+2)$, you would multiply $7$ by each term inside the parentheses: $7q$, $21$, and $14$.

Q: How do I simplify expressions after multiplying?

A: After multiplying expressions, you need to simplify the result by combining like terms. For example, if you have $7q + 21 + 14$, you would combine the like terms: $7q + 35$.

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

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

• Forgetting to distribute: Make sure to multiply each term inside the parentheses by the single term outside the parentheses.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
• Not combining like terms: Make sure to combine like terms when simplifying expressions.

Q: Can I use the distributive property with fractions?

A: Yes, you can use the distributive property with fractions. For example, if you have $\frac{1}{2}(x+3)$, you would multiply $\frac{1}{2}$ by each term inside the parentheses: $\frac{1}{2}x$ and $\frac{3}{2}$.

Q: How do I multiply expressions with negative numbers?

A: When multiplying expressions with negative numbers, you need to follow the rules of multiplication with negative numbers. For example, if you have $-7(q+3)$, you would multiply $-7$ by each term inside the parentheses: $-7q$ and $-21$.

Conclusion

In this article, we have answered some common questions that students often have when multiplying expressions. We have covered topics such as the distributive property, applying the distributive property, and simplifying expressions after multiplying. By following these steps and using the distributive property, we can simplify complex expressions and solve problems in algebra.

Practice Problems

To reinforce your understanding of multiplying expressions, try the following practice problems:

Problem 1: Multiply $3$ by $(x+2)$

Using the distributive property, multiply $3$ by each term inside the parentheses.

Problem 2: Multiply $2$ by $(y-4)$

Using the distributive property, multiply $2$ by each term inside the parentheses.

Problem 3: Multiply $5$ by $(z+1)$

Using the distributive property, multiply $5$ by each term inside the parentheses.

Answer Key

Problem 1: Multiply $3$ by $(x+2)$

$3(x+2) = 3x + 6$

Problem 2: Multiply $2$ by $(y-4)$

$2(y-4) = 2y - 8$

Problem 3: Multiply $5$ by $(z+1)$

$5(z+1) = 5z + 5$