Simplify The Expression: 7 P + 3 N − P + N 7p + 3n - P + N 7 P + 3 N − P + N

$$

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, which are terms that have the same variable raised to the same power. In this article, we will simplify the expression $7p + 3n - p + n$ using the rules of algebra.

Understanding Like Terms

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. On the other hand, $2x$ and $3y$ are not like terms because they have different variables.

Simplifying the Expression

To simplify the expression $7p + 3n - p + n$, we need to combine like terms. The expression can be rewritten as:

$$7p - p + 3n + n$$

Now, we can combine the like terms:

$$6p + 4n$$

Step-by-Step Solution

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

1. Identify the like terms: The like terms in the expression are $7p$ and $-p$, and $3n$ and $n$.
2. Combine the like terms: We can combine the like terms by adding or subtracting their coefficients.
3. Simplify the expression: After combining the like terms, we get $6p + 4n$.

Example

Let's consider an example to illustrate the concept of simplifying expressions. Suppose we have the expression $2x + 3y - 4x + 2y$. We can simplify this expression by combining the like terms:

$$2x - 4x + 3y + 2y$$

$$-2x + 5y$$

Tips and Tricks

Here are some tips and tricks to help you simplify expressions:

• Identify the like terms: The first step in simplifying an expression is to identify the like terms.
• Combine the like terms: Once you have identified the like terms, you can combine them by adding or subtracting their coefficients.
• Simplify the expression: After combining the like terms, you should simplify the expression to get the final result.

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By combining like terms, we can simplify expressions and get the final result. In this article, we simplified the expression $7p + 3n - p + n$ using the rules of algebra. We also provided a step-by-step solution and some tips and tricks to help you simplify expressions.

Frequently Asked Questions

Here are some frequently asked questions about simplifying expressions:

• What are like terms?: Like terms are terms that have the same variable raised to the same power.
• How do I simplify an expression?: To simplify an expression, you need to identify the like terms and combine them by adding or subtracting their coefficients.
• What is the final result of simplifying an expression?: The final result of simplifying an expression is a simplified expression that has no like terms.

References

• Algebra for Dummies: This book provides a comprehensive introduction to algebra, including simplifying expressions.
• Mathematics for Elementary Teachers: This book provides a comprehensive introduction to mathematics, including algebra and simplifying expressions.

Further Reading

If you want to learn more about simplifying expressions, here are some further reading resources:

• Simplifying Expressions: This article provides a comprehensive introduction to simplifying expressions.
• Algebraic Expressions: This article provides a comprehensive introduction to algebraic expressions, including simplifying expressions.
• Mathematics for Elementary Teachers: This book provides a comprehensive introduction to mathematics, including algebra and simplifying expressions.
  Simplify the Expression: $7p + 3n - p + n$ - Q&A =====================================================

Introduction

In our previous article, we simplified the expression $7p + 3n - p + n$ using the rules of algebra. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

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 simplify an expression?

A: To simplify an expression, you need to identify the like terms and combine them by adding or subtracting their coefficients. For example, to simplify the expression $7p + 3n - p + n$, you would combine the like terms as follows:

$$7p - p + 3n + n$$

$$6p + 4n$$

Q: What is the final result of simplifying an expression?

A: The final result of simplifying an expression is a simplified expression that has no like terms. In the example above, the final result is $6p + 4n$.

Q: Can I simplify an expression with variables of different powers?

A: No, you cannot simplify an expression with variables of different powers. For example, the expression $2x^2 + 3x$ cannot be simplified because the variables have different powers.

Q: Can I simplify an expression with variables of different bases?

A: No, you cannot simplify an expression with variables of different bases. For example, the expression $2x + 3y$ cannot be simplified because the variables have different bases.

Q: How do I know if an expression can be simplified?

A: To determine if an expression can be simplified, you need to check if there are any like terms. If there are like terms, you can simplify the expression by combining them.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions. For example, the expression $\frac{2x}{3} + \frac{3x}{4}$ can be simplified as follows:

$$\frac{2x}{3} + \frac{3x}{4} = \frac{8x + 9x}{12} = \frac{17x}{12}$$

Q: Can I simplify an expression with decimals?

A: Yes, you can simplify an expression with decimals. For example, the expression $2.5x + 3.2x$ can be simplified as follows:

$$2.5x + 3.2x = 5.7x$$

Q: Can I simplify an expression with negative numbers?

A: Yes, you can simplify an expression with negative numbers. For example, the expression $-2x + 3x$ can be simplified as follows:

$$-2x + 3x = x$$

Q: Can I simplify an expression with parentheses?

A: Yes, you can simplify an expression with parentheses. For example, the expression $(2x + 3x)$ can be simplified as follows:

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

Q: Can I simplify an expression with exponents?

A: Yes, you can simplify an expression with exponents. For example, the expression $2x^2 + 3x^2$ can be simplified as follows:

$$2x^2 + 3x^2 = 5x^2$$

Q: Can I simplify an expression with radicals?

A: Yes, you can simplify an expression with radicals. For example, the expression $\sqrt{2x} + \sqrt{3x}$ can be simplified as follows:

$$\sqrt{2x} + \sqrt{3x} = \sqrt{2x + 3x} = \sqrt{5x}$$

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By combining like terms, we can simplify expressions and get the final result. In this article, we answered some frequently asked questions about simplifying expressions.

Frequently Asked Questions

Here are some frequently asked questions about simplifying expressions:

• What are like terms?
• How do I simplify an expression?
• What is the final result of simplifying an expression?
• Can I simplify an expression with variables of different powers?
• Can I simplify an expression with variables of different bases?
• How do I know if an expression can be simplified?
• Can I simplify an expression with fractions?
• Can I simplify an expression with decimals?
• Can I simplify an expression with negative numbers?
• Can I simplify an expression with parentheses?
• Can I simplify an expression with exponents?
• Can I simplify an expression with radicals?

References

• Algebra for Dummies: This book provides a comprehensive introduction to algebra, including simplifying expressions.
• Mathematics for Elementary Teachers: This book provides a comprehensive introduction to mathematics, including algebra and simplifying expressions.

Further Reading

If you want to learn more about simplifying expressions, here are some further reading resources:

• Simplifying Expressions: This article provides a comprehensive introduction to simplifying expressions.
• Algebraic Expressions: This article provides a comprehensive introduction to algebraic expressions, including simplifying expressions.
• Mathematics for Elementary Teachers: This book provides a comprehensive introduction to mathematics, including algebra and simplifying expressions.