Solve The Expression: ( P + Q ) ( 2 ) = (p+q)(2)= ( P + Q ) ( 2 ) =

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Introduction

In mathematics, algebraic expressions are a fundamental concept that helps us solve various problems. One of the essential skills in algebra is to simplify and solve expressions involving variables and constants. In this article, we will focus on solving the expression $(p+q)(2)=$, which involves the multiplication of a binomial and a constant.

Understanding the Expression

The given expression is $(p+q)(2)=$, where $p$ and $q$ are variables, and $2$ is a constant. To solve this expression, 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 $(p+q)(2)$, which can be expanded using the distributive property.

Applying the Distributive Property

Using the distributive property, we can expand the expression $(p+q)(2)$ as follows:

$(p+q)(2) = p(2) + q(2)$

This can be further simplified as:

$2p + 2q$

Simplifying the Expression

Now that we have expanded the expression, we can simplify it by combining like terms. In this case, we have $2p + 2q$, which can be rewritten as:

$2(p + q)$

This is the simplified form of the expression $(p+q)(2)=$.

Conclusion

In conclusion, solving the expression $(p+q)(2)=$ involves applying the distributive property and simplifying the resulting expression. By following these steps, we can simplify the expression and arrive at the final answer. This problem is an essential concept in algebra, and understanding how to solve it will help you tackle more complex problems in the future.

Real-World Applications

The concept of solving expressions like $(p+q)(2)=$ has numerous real-world applications. For example, in physics, the expression $2p + 2q$ can represent the total energy of a system, where $p$ and $q$ are the kinetic and potential energies, respectively. In economics, the expression $2(p + q)$ can represent the total cost of producing a product, where $p$ and $q$ are the costs of labor and materials, respectively.

Tips and Tricks

Here are some tips and tricks to help you solve expressions like $(p+q)(2)=$:

• Always apply the distributive property when multiplying a binomial and a constant.
• Simplify the resulting expression by combining like terms.
• Use the commutative property of addition to rearrange the terms in the expression.
• Use the associative property of addition to group the terms in the expression.

Practice Problems

Here are some practice problems to help you reinforce your understanding of solving expressions like $(p+q)(2)=$:

• Solve the expression $(x+y)(3)=$.
• Solve the expression $(a+b)(4)=$.
• Solve the expression $(c+d)(2)=$.

Common Mistakes

Here are some common mistakes to avoid when solving expressions like $(p+q)(2)=$:

• Failing to apply the distributive property when multiplying a binomial and a constant.
• Not simplifying the resulting expression by combining like terms.
• Using the distributive property incorrectly, such as multiplying the constant with only one of the variables.

Final Thoughts

Solving expressions like $(p+q)(2)=$ is an essential skill in algebra that has numerous real-world applications. By understanding how to apply the distributive property and simplify the resulting expression, you can tackle more complex problems in the future. Remember to always practice and reinforce your understanding of these concepts to become proficient in solving expressions like $(p+q)(2)=$.

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Introduction

In our previous article, we discussed how to solve the expression $(p+q)(2)=$ by applying the distributive property and simplifying the resulting expression. However, we know that practice makes perfect, and the best way to reinforce your understanding of this concept is to try out some practice problems and ask questions. In this article, we will provide a Q&A section where we will answer some common questions and provide additional practice problems to help you become proficient in solving expressions like $(p+q)(2)=$.

Q&A

Q: What is the distributive property, and how is it used to solve expressions like $(p+q)(2)=$?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. This property is used to expand expressions like $(p+q)(2)$ by multiplying the constant with each of the variables.

Q: How do I simplify the expression $(p+q)(2)=$?

A: To simplify the expression $(p+q)(2)=$, you need to apply the distributive property and then combine like terms. The resulting expression is $2p + 2q$, which can be rewritten as $2(p + q)$.

Q: What are some common mistakes to avoid when solving expressions like $(p+q)(2)=$?

A: Some common mistakes to avoid when solving expressions like $(p+q)(2)=$ include:

• Failing to apply the distributive property when multiplying a binomial and a constant.
• Not simplifying the resulting expression by combining like terms.
• Using the distributive property incorrectly, such as multiplying the constant with only one of the variables.

Q: Can you provide some practice problems to help me become proficient in solving expressions like $(p+q)(2)=$?

A: Here are some practice problems to help you become proficient in solving expressions like $(p+q)(2)=$:

• Solve the expression $(x+y)(3)=$.
• Solve the expression $(a+b)(4)=$.
• Solve the expression $(c+d)(2)=$.

Q: How do I know if I have simplified the expression correctly?

A: To ensure that you have simplified the expression correctly, you need to check that you have applied the distributive property and combined like terms. You can also use the commutative property of addition to rearrange the terms in the expression and the associative property of addition to group the terms in the expression.

Additional Practice Problems

Here are some additional practice problems to help you become proficient in solving expressions like $(p+q)(2)=$:

• Solve the expression $(2x+3y)(4)=$.
• Solve the expression $(a+b+c)(2)=$.
• Solve the expression $(p+q+r)(3)=$.

Tips and Tricks

Here are some tips and tricks to help you solve expressions like $(p+q)(2)=$:

• Always apply the distributive property when multiplying a binomial and a constant.
• Simplify the resulting expression by combining like terms.
• Use the commutative property of addition to rearrange the terms in the expression.
• Use the associative property of addition to group the terms in the expression.

Conclusion

Solving expressions like $(p+q)(2)=$ is an essential skill in algebra that has numerous real-world applications. By understanding how to apply the distributive property and simplify the resulting expression, you can tackle more complex problems in the future. Remember to always practice and reinforce your understanding of these concepts to become proficient in solving expressions like $(p+q)(2)=$.