Add And Subtract BinomialsQuestion: Rewrite In Simplest Terms: { (3r + 10)(62)$}$Answer: { \square$}$

Introduction

In algebra, binomials are a type of polynomial that consists of two terms. When we are given two binomials, we can perform various operations such as addition, subtraction, multiplication, and division. In this article, we will focus on adding and subtracting binomials, which is a fundamental concept in algebra. We will explore the steps involved in adding and subtracting binomials, provide examples, and offer tips for simplifying expressions.

What are Binomials?

A binomial is a polynomial that consists of two terms. It can be written in the form of $ax + b$, where $a$ and $b$ are constants, and $x$ is the variable. For example, $3x + 2$ and $5x - 3$ are both binomials.

Adding Binomials

When we add two binomials, we need to combine like terms. Like terms are terms that have the same variable and coefficient. To add binomials, we follow these steps:

1. Distribute the terms: We need to distribute each term in the first binomial to each term in the second binomial.
2. Combine like terms: We combine the like terms to simplify the expression.

Example 1: Adding Binomials

Let's consider the following example:

${(3r + 10)(62)}$

To add these binomials, we need to distribute the terms and combine like terms.

Step 1: Distribute the terms

${(3r + 10)(62) = 3r(62) + 10(62)}$

Step 2: Combine like terms

${3r(62) + 10(62) = 186r + 620}$

Therefore, the simplified expression is $186r + 620$.

Subtracting Binomials

When we subtract two binomials, we need to combine like terms. To subtract binomials, we follow these steps:

1. Distribute the terms: We need to distribute each term in the first binomial to each term in the second binomial.
2. Combine like terms: We combine the like terms to simplify the expression.

Example 2: Subtracting Binomials

Let's consider the following example:

${(5x - 3) - (2x + 4)}$

To subtract these binomials, we need to distribute the terms and combine like terms.

Step 1: Distribute the terms

${(5x - 3) - (2x + 4) = 5x - 3 - 2x - 4}$

Step 2: Combine like terms

${5x - 3 - 2x - 4 = 3x - 7}$

Therefore, the simplified expression is $3x - 7$.

Tips for Simplifying Expressions

When simplifying expressions, we need to combine like terms. To combine like terms, we need to follow these steps:

1. Identify like terms: We need to identify the like terms in the expression.
2. Combine the coefficients: We need to combine the coefficients of the like terms.
3. Keep the variable the same: We need to keep the variable the same.

Example 3: Simplifying an Expression

Let's consider the following example:

${2x + 3x + 4 - 2}$

To simplify this expression, we need to combine like terms.

Step 1: Identify like terms

The like terms in this expression are $2x$ and $3x$.

Step 2: Combine the coefficients

The coefficients of the like terms are $2$ and $3$. We need to combine these coefficients.

Step 3: Keep the variable the same

We need to keep the variable $x$ the same.

Therefore, the simplified expression is $5x + 2$.

Conclusion

In this article, we have discussed the concept of adding and subtracting binomials. We have explored the steps involved in adding and subtracting binomials, provided examples, and offered tips for simplifying expressions. We have also discussed the importance of combining like terms when simplifying expressions. By following these steps and tips, we can simplify expressions and solve algebraic problems with ease.

Final Answer

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Q&A: Frequently Asked Questions

Q: What are binomials?

A: A binomial is a polynomial that consists of two terms. It can be written in the form of $ax + b$, where $a$ and $b$ are constants, and $x$ is the variable.

Q: How do I add binomials?

A: To add binomials, you need to combine like terms. Like terms are terms that have the same variable and coefficient. To add binomials, follow these steps:

1. Distribute the terms: Distribute each term in the first binomial to each term in the second binomial.
2. Combine like terms: Combine the like terms to simplify the expression.

Q: How do I subtract binomials?

A: To subtract binomials, you need to combine like terms. To subtract binomials, follow these steps:

1. Distribute the terms: Distribute each term in the first binomial to each term in the second binomial.
2. Combine like terms: Combine the like terms to simplify the expression.

Q: What are like terms?

A: Like terms are terms that have the same variable and coefficient. For example, $2x$ and $3x$ are like terms because they have the same variable $x$ and coefficients $2$ and $3$.

Q: How do I combine like terms?

A: To combine like terms, follow these steps:

1. Identify like terms: Identify the like terms in the expression.
2. Combine the coefficients: Combine the coefficients of the like terms.
3. Keep the variable the same: Keep the variable the same.

Q: What is the difference between adding and subtracting binomials?

A: The main difference between adding and subtracting binomials is that when you add binomials, you are combining the terms to get a larger value, while when you subtract binomials, you are combining the terms to get a smaller value.

Q: Can I add or subtract binomials with different variables?

A: No, you cannot add or subtract binomials with different variables. Binomials must have the same variable to be added or subtracted.

Q: How do I simplify expressions with binomials?

A: To simplify expressions with binomials, follow these steps:

1. Distribute the terms: Distribute each term in the first binomial to each term in the second binomial.
2. Combine like terms: Combine the like terms to simplify the expression.

Q: What are some common mistakes to avoid when adding and subtracting binomials?

A: Some common mistakes to avoid when adding and subtracting binomials include:

• Not distributing the terms correctly
• Not combining like terms correctly
• Not keeping the variable the same
• Not simplifying the expression correctly

Conclusion

In this article, we have discussed the concept of adding and subtracting binomials, provided examples, and offered tips for simplifying expressions. We have also discussed the importance of combining like terms when simplifying expressions. By following these steps and tips, we can simplify expressions and solve algebraic problems with ease.

Final Answer

The final answer is $\boxed{186r + 620}$.