Simplify The Expression: 3 C + 2 C × 4 C + C + ( 5 C − 8 C 3c + 2c \times 4c + C + (5c - 8c 3 C + 2 C × 4 C + C + ( 5 C − 8 C ]

Mar 9, 2025 by ADMIN 128 views

$Simplify the Expression: $3c + 2c \times 4c + c + (5c - 8c)$$

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to solve problems more efficiently. It involves combining like terms and eliminating any unnecessary operations. In this article, we will focus on simplifying the given expression: $3c + 2c \times 4c + c + (5c - 8c)$ . We will use the order of operations (PEMDAS) and combine like terms to simplify the expression.

Understanding the Order of Operations

Before we start simplifying the expression, it's essential to understand the order of operations, which is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

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

Simplifying the Expression

Now that we understand the order of operations, let's simplify the given expression:

$3c + 2c \times 4c + c + (5c - 8c)$

First, we need to evaluate the expression inside the parentheses:

$(5c - 8c) = -3c$

Now, the expression becomes:

$3c + 2c \times 4c + c - 3c$

Next, we need to evaluate the multiplication operation:

$2c \times 4c = 8c^2$

Now, the expression becomes:

$3c + 8c^2 + c - 3c$

Combining Like Terms

Now that we have evaluated all the operations, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable $c$ :

$3c + c - 3c$

We can combine these terms by adding or subtracting their coefficients:

$3c + c - 3c = (3 + 1 - 3)c = 1c$

So, the expression simplifies to:

$8c^2 + 1c$

Final Simplified Expression

The final simplified expression is:

$8c^2 + c$

Conclusion

In this article, we simplified the given expression: $3c + 2c \times 4c + c + (5c - 8c)$ . We used the order of operations (PEMDAS) and combined like terms to simplify the expression. The final simplified expression is $8c^2 + c$ . This example demonstrates the importance of simplifying expressions in mathematics, as it helps us to solve problems more efficiently and accurately.

Tips and Tricks

When simplifying expressions, always follow the order of operations (PEMDAS).
Combine like terms by adding or subtracting their coefficients.
Use parentheses to group terms and make it easier to simplify the expression.

Common Mistakes to Avoid

Failing to follow the order of operations (PEMDAS).
Not combining like terms.
Not using parentheses to group terms.

Real-World Applications

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. For example:

In physics, simplifying expressions is used to solve problems involving motion, energy, and momentum.
In engineering, simplifying expressions is used to design and optimize systems.
In economics, simplifying expressions is used to model and analyze economic systems.

Practice Problems

Try simplifying the following expressions:

$2x + 3x - 4x$
$5y \times 2y + y - 3y$
$6z + 2z \times 3z + z - 2z$

Solutions

$2x + 3x - 4x = (2 + 3 - 4)x = 1x$
$5y \times 2y + y - 3y = 10y^2 + y - 3y = 10y^2 - 2y$
$6z + 2z \times 3z + z - 2z = 6z + 6z^2 + z - 2z = 6z^2 + 4z$

Conclusion

Simplifying expressions is a crucial skill in mathematics that has many real-world applications. By following the order of operations (PEMDAS) and combining like terms, we can simplify complex expressions and solve problems more efficiently and accurately.

Introduction

In our previous article, we simplified the expression: $3c + 2c \times 4c + c + (5c - 8c)$ . We used the order of operations (PEMDAS) and combined like terms to simplify the expression. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

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

Q: How do I simplify an expression with multiple operations?

A: To simplify an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $3x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, if we have the expression $2x + 3x$ , we can combine the like terms by adding their coefficients: $2x + 3x = (2 + 3)x = 5x$ .

Q: What is the difference between a coefficient and a variable?

A: A coefficient is a number that is multiplied by a variable. For example, in the expression $2x$ , the coefficient is 2 and the variable is $x$ . A variable is a letter or symbol that represents a value.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, follow the same steps as before. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the final simplified expression?

A: The final simplified expression is $8c^2 + c$ .