Evaluate:$3 \cdot (1+3)^2$

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Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by applying the order of operations. The expression $3 \cdot (1+3)^2$ is a simple algebraic expression that requires careful evaluation to obtain the correct result. In this article, we will evaluate the expression $3 \cdot (1+3)^2$ step by step, using the order of operations to simplify the expression.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

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

Evaluating the Expression

To evaluate the expression $3 \cdot (1+3)^2$, we will follow the order of operations.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is $1+3$. To evaluate this expression, we simply add 1 and 3 together.

$1+3 = 4$

So, the expression inside the parentheses is equal to 4.

Step 2: Raise 4 to the Power of 2

The expression $(1+3)^2$ is equivalent to $4^2$. To evaluate this expression, we raise 4 to the power of 2.

$4^2 = 16$

So, the expression $(1+3)^2$ is equal to 16.

Step 3: Multiply 3 by 16

The final step is to multiply 3 by 16.

$3 \cdot 16 = 48$

Therefore, the value of the expression $3 \cdot (1+3)^2$ is 48.

Conclusion

In this article, we evaluated the expression $3 \cdot (1+3)^2$ step by step, using the order of operations to simplify the expression. We first evaluated the expression inside the parentheses, then raised the result to the power of 2, and finally multiplied the result by 3. The final value of the expression is 48.

Frequently Asked Questions

Q: What is the order of operations? A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS.

Q: How do I evaluate an expression with parentheses? A: To evaluate an expression with parentheses, you should first evaluate the expression inside the parentheses, then proceed with the rest of the expression.

Q: What is the value of the expression $3 \cdot (1+3)^2$? A: The value of the expression $3 \cdot (1+3)^2$ is 48.

Further Reading

• For more information on the order of operations, see the article "Understanding the Order of Operations".
• For more information on evaluating expressions with parentheses, see the article "Evaluating Expressions with Parentheses".
• For more information on algebraic expressions, see the article "Algebraic Expressions: A Comprehensive Guide".
  

Introduction

Evaluating expressions is a fundamental concept in mathematics that involves simplifying mathematical expressions by applying the order of operations. In our previous article, we evaluated the expression $3 \cdot (1+3)^2$ step by step, using the order of operations to simplify the expression. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A Guide

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any 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 evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, you should first evaluate the expression inside the parentheses, then proceed with the rest of the expression. For example, to evaluate the expression $(2+3)^2$, you would first evaluate the expression inside the parentheses, which is $2+3=5$. Then, you would raise 5 to the power of 2, which is $5^2=25$.

Q: What is the value of the expression $3 \cdot (1+3)^2$?

A: The value of the expression $3 \cdot (1+3)^2$ is 48. To evaluate this expression, you would first evaluate the expression inside the parentheses, which is $1+3=4$. Then, you would raise 4 to the power of 2, which is $4^2=16$. Finally, you would multiply 3 by 16, which is $3 \cdot 16=48$.

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

A: To evaluate an expression with multiple operations, you should follow the order of operations. For example, to evaluate the expression $3 \cdot 2 + 4$, you would first multiply 3 by 2, which is $3 \cdot 2=6$. Then, you would add 4 to 6, which is $6+4=10$.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables and constants, but does not contain an equal sign. An equation is a mathematical statement that contains an equal sign and is used to solve for a variable. For example, the expression $2x+3$ is a mathematical statement that contains a variable and a constant, but does not contain an equal sign. The equation $2x+3=5$ is a mathematical statement that contains an equal sign and is used to solve for the variable x.

Q: How do I simplify an expression?

A: To simplify an expression, you should combine like terms and eliminate any unnecessary operations. For example, to simplify the expression $2x+3+2x$, you would combine the like terms $2x$ and $2x$, which is $4x$. Then, you would add 3 to $4x$, which is $4x+3$.

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions. We covered topics such as the order of operations, evaluating expressions with parentheses, and simplifying expressions. We hope that this article has been helpful in clarifying any confusion you may have had about evaluating expressions.

Further Reading

• For more information on the order of operations, see the article "Understanding the Order of Operations".
• For more information on evaluating expressions with parentheses, see the article "Evaluating Expressions with Parentheses".
• For more information on algebraic expressions, see the article "Algebraic Expressions: A Comprehensive Guide".

Common Mistakes to Avoid

• Not following the order of operations
• Not evaluating expressions inside parentheses first
• Not combining like terms
• Not eliminating unnecessary operations

Tips for Evaluating Expressions

• Read the expression carefully and identify the operations
• Follow the order of operations
• Evaluate expressions inside parentheses first
• Combine like terms
• Eliminate unnecessary operations

Practice Problems

• Evaluate the expression $(2+3)^2$
• Evaluate the expression $3 \cdot (1+3)^2$
• Simplify the expression $2x+3+2x$
• Evaluate the expression $3 \cdot 2 + 4$

Solutions to Practice Problems

• $(2+3)^2 = 5^2 = 25$
• $3 \cdot (1+3)^2 = 3 \cdot 4^2 = 3 \cdot 16 = 48$
• $2x+3+2x = 4x+3$
• $3 \cdot 2 + 4 = 6 + 4 = 10$