Evaluating the Answer Choices

Oct 13, 2025 by pynkocean.com 23 views

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, with a focus on combining like terms. We will also examine a specific problem, which asks us to find the equivalent expression for $$5c + 8c$$.

What are Algebraic Expressions?

Algebraic expressions are a combination of variables, constants, and mathematical operations. They can be represented using variables, such as x, y, or c, and can include constants, like 2, 5, or 10. Algebraic expressions can also involve mathematical operations, such as addition, subtraction, multiplication, and division.

Combining Like Terms

Like terms are algebraic expressions that have the same variable raised to the same power. When we combine like terms, we add or subtract the coefficients of the like terms. For example, consider the expression $$3x + 2x$$. In this case, we can combine the like terms by adding the coefficients:

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

Simplifying the Expression $$5c + 8c$$

Now, let's apply the concept of combining like terms to the expression $$5c + 8c$$. In this case, we have two like terms, both of which involve the variable c. To simplify the expression, we can combine the like terms by adding the coefficients:

5c + 8c = (5 + 8)c = 13c

Evaluating the Answer Choices

Now that we have simplified the expression $$5c + 8c$$, let's evaluate the answer choices:

A. $$c + 13$$: This expression is not equivalent to $$5c + 8c$$, as it involves a different variable and a constant.
B. $$12c$$: This expression is not equivalent to $$5c + 8c$$, as it involves a different coefficient.
C. $$13c$$: This expression is equivalent to $$5c + 8c$$, as it involves the same variable and coefficient.
D. $$c^{13}$$: This expression is not equivalent to $$5c + 8c$$, as it involves a different variable and a different exponent.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By combining like terms, we can simplify complex expressions and make them easier to work with. In this article, we applied the concept of combining like terms to the expression $$5c + 8c$$ and found that the equivalent expression is $$13c$$. We also evaluated the answer choices and determined that only one of them is equivalent to the original expression.

Additional Tips and Resources

When simplifying algebraic expressions, always look for like terms and combine them by adding or subtracting the coefficients.
Use the distributive property to simplify expressions involving parentheses.
Practice simplifying algebraic expressions by working through example problems and exercises.

Common Algebraic Expressions

Here are some common algebraic expressions that you may encounter:

$2x + 3$
$x^2 + 4x + 5$
$\frac{x}{2} + 3$
$x^2 - 4x + 5$

Step 1: Identify Like Terms

Like terms are algebraic expressions that have the same variable raised to the same power. When we combine like terms, we add or subtract the coefficients of the like terms.

Step 2: Combine Like Terms

To combine like terms, we add or subtract the coefficients of the like terms. For example, consider the expression $$3x + 2x$$. In this case, we can combine the like terms by adding the coefficients:

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

Step 3: Simplify the Expression

Once we have combined the like terms, we can simplify the expression by applying the distributive property and combining any remaining like terms.

Step 4: Evaluate the Answer Choices

Finally, we can evaluate the answer choices and determine which one is equivalent to the original expression.

Conclusion

Additional Tips and Resources

When simplifying algebraic expressions, always look for like terms and combine them by adding or subtracting the coefficients.
Use the distributive property to simplify expressions involving parentheses.
Practice simplifying algebraic expressions by working through example problems and exercises.

Common Algebraic Expressions

Here are some common algebraic expressions that you may encounter:

$2x + 3$
$x^2 + 4x + 5$
$\frac{x}{2} + 3$
$x^2 - 4x + 5$

Final Answer

$The final answer is: $\boxed{13c}$<br/> **Simplifying Algebraic Expressions: A Q&A Guide**$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In our previous article, we explored the process of simplifying algebraic expressions, with a focus on combining like terms. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What are like terms?

A: Like terms are algebraic expressions that have the same variable raised to the same power. When we combine like terms, we add or subtract the coefficients of the like terms.

Q: How do I identify like terms?

A: To identify like terms, look for expressions that have the same variable raised to the same power. For example, consider the expression $$3x + 2x$$. In this case, we can identify the like terms as $$3x$$ and $$2x$$.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, consider the expression $$3x + 2x$$. In this case, we can combine the like terms by adding the coefficients:

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

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to multiply a single term by multiple terms. For example, consider the expression $$2(x + 3)$$. Using the distributive property, we can rewrite the expression as:

2(x + 3) = 2x + 6

Q: How do I simplify expressions involving parentheses?

A: To simplify expressions involving parentheses, use the distributive property to multiply the terms inside the parentheses by the term outside the parentheses. For example, consider the expression $$2(x + 3)$$. Using the distributive property, we can rewrite the expression as:

2(x + 3) = 2x + 6

Q: What are some common algebraic expressions?

A: Here are some common algebraic expressions that you may encounter:

$2x + 3$
$x^2 + 4x + 5$
$\frac{x}{2} + 3$
$x^2 - 4x + 5$

Q: How do I practice simplifying algebraic expressions?

A: To practice simplifying algebraic expressions, work through example problems and exercises. You can also try simplifying expressions on your own and then check your answers with a calculator or a math book.

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

A: Here are some common mistakes to avoid when simplifying algebraic expressions:

Not identifying like terms
Not combining like terms correctly
Not using the distributive property to simplify expressions involving parentheses
Not checking your answers with a calculator or a math book

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By combining like terms, using the distributive property, and practicing regularly, you can become proficient in simplifying algebraic expressions. In this article, we answered some frequently asked questions about simplifying algebraic expressions and provided some common algebraic expressions for you to practice with.

Additional Tips and Resources

When simplifying algebraic expressions, always look for like terms and combine them by adding or subtracting the coefficients.
Use the distributive property to simplify expressions involving parentheses.
Practice simplifying algebraic expressions by working through example problems and exercises.
Check your answers with a calculator or a math book to ensure accuracy.

Common Algebraic Expressions

Here are some common algebraic expressions that you may encounter:

$2x + 3$
$x^2 + 4x + 5$
$\frac{x}{2} + 3$
$x^2 - 4x + 5$

Final Answer

The final answer is: $\boxed{13c}$