Use Your Result From The Sum:1. $6ab^2$2. $3ab + 3b^2$3. $-6a^2 + 3ab + 3b^2$4. $-6a^2 - 13ab + 3b^2$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore the process of solving algebraic expressions, focusing on the given expressions: $6ab^2$, $3ab + 3b^2$, $-6a^2 + 3ab + 3b^2$, and $-6a^2 - 13ab + 3b^2$. We will break down each expression, identify the like terms, and combine them to simplify the expression.

Understanding Algebraic Expressions

An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using symbols and mathematical notation. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.

Like Terms and Combining Like Terms

Like terms are terms that have the same variable(s) raised to the same power. In other words, like terms are terms that have the same base and exponent. When combining like terms, we add or subtract the coefficients of the like terms. The coefficients are the numerical values that are multiplied by the variables.

Solving Expression 1: $6ab^2$

The given expression is $6ab^2$. This expression has one term, which is $6ab^2$. Since there are no like terms, the expression is already simplified.

Solving Expression 2: $3ab + 3b^2$

The given expression is $3ab + 3b^2$. This expression has two terms: $3ab$ and $3b^2$. We can identify the like terms by looking at the variables and their exponents. In this case, the like terms are $3ab$ and $3b^2$. We can combine these like terms by adding their coefficients.

Step 1: Identify the Like Terms

The like terms in the expression $3ab + 3b^2$ are $3ab$ and $3b^2$.

Step 2: Combine the Like Terms

We can combine the like terms by adding their coefficients. The coefficient of $3ab$ is 3, and the coefficient of $3b^2$ is also 3. Since the variables are the same, we can add the coefficients.

Step 3: Simplify the Expression

The combined like terms are $6b^2$. Therefore, the simplified expression is $6b^2$.

Solving Expression 3: $-6a^2 + 3ab + 3b^2$

The given expression is $-6a^2 + 3ab + 3b^2$. This expression has three terms: $-6a^2$, $3ab$, and $3b^2$. We can identify the like terms by looking at the variables and their exponents. In this case, the like terms are $-6a^2$ and $3ab$, and $3b^2$.

Step 1: Identify the Like Terms

The like terms in the expression $-6a^2 + 3ab + 3b^2$ are $-6a^2$ and $3ab$, and $3b^2$.

Step 2: Combine the Like Terms

We can combine the like terms by adding their coefficients. The coefficient of $-6a^2$ is -6, the coefficient of $3ab$ is 3, and the coefficient of $3b^2$ is 3. Since the variables are the same, we can add the coefficients.

Step 3: Simplify the Expression

The combined like terms are $-3a^2 + 3b^2$. Therefore, the simplified expression is $-3a^2 + 3b^2$.

Solving Expression 4: $-6a^2 - 13ab + 3b^2$

The given expression is $-6a^2 - 13ab + 3b^2$. This expression has three terms: $-6a^2$, $-13ab$, and $3b^2$. We can identify the like terms by looking at the variables and their exponents. In this case, the like terms are $-6a^2$ and $-13ab$, and $3b^2$.

Step 1: Identify the Like Terms

The like terms in the expression $-6a^2 - 13ab + 3b^2$ are $-6a^2$ and $-13ab$, and $3b^2$.

Step 2: Combine the Like Terms

We can combine the like terms by adding their coefficients. The coefficient of $-6a^2$ is -6, the coefficient of $-13ab$ is -13, and the coefficient of $3b^2$ is 3. Since the variables are the same, we can add the coefficients.

Step 3: Simplify the Expression

The combined like terms are $-6a^2 - 13ab + 3b^2$. Therefore, the simplified expression is $-6a^2 - 13ab + 3b^2$.

Conclusion

In this article, we have explored the process of solving algebraic expressions, focusing on the given expressions: $6ab^2$, $3ab + 3b^2$, $-6a^2 + 3ab + 3b^2$, and $-6a^2 - 13ab + 3b^2$. We have identified the like terms, combined them, and simplified the expressions. By following these steps, we can simplify complex algebraic expressions and solve mathematical problems with ease.

Final Answer

The final answers to the given expressions are:

• $6ab^2$
• $6b^2$
• $-3a^2 + 3b^2$
• $-6a^2 - 13ab + 3b^2$

Note: The final answer for expression 4 is the same as the original expression, which means that the expression cannot be simplified further.

Introduction

Algebraic expressions are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will answer some frequently asked questions about algebraic expressions, focusing on the process of solving them.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using symbols and mathematical notation.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. In other words, like terms are terms that have the same base and exponent.

Q: How do I identify like terms?

A: To identify like terms, look at the variables and their exponents in each term. If the variables are the same and the exponents are the same, then the terms are like terms.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. The coefficients are the numerical values that are multiplied by the variables.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms is the process of adding or subtracting the coefficients of like terms, while simplifying an expression is the process of reducing an expression to its simplest form by combining like terms and eliminating any unnecessary terms.

Q: Can an expression be simplified further if it has been combined?

A: Yes, an expression can be simplified further if it has been combined. For example, if an expression has been combined to $2x + 3x$, it can be simplified further to $5x$.

Q: What is the importance of simplifying algebraic expressions?

A: Simplifying algebraic expressions is important because it helps to:

• Reduce the complexity of an expression
• Make it easier to solve equations and inequalities
• Identify patterns and relationships between variables
• Make it easier to communicate mathematical ideas and concepts

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

A: To determine if an expression can be simplified further, look for like terms and combine them. If the expression has been combined and there are no like terms left, then it cannot be simplified further.

Q: Can an expression be simplified if it has a negative sign?

A: Yes, an expression can be simplified even if it has a negative sign. For example, if an expression is $-3x + 2x$, it can be simplified to $-x$.

Q: What is the final answer to the given expressions?

A: The final answers to the given expressions are:

• $6ab^2$
• $6b^2$
• $-3a^2 + 3b^2$
• $-6a^2 - 13ab + 3b^2$

Note: The final answer for expression 4 is the same as the original expression, which means that the expression cannot be simplified further.

Conclusion

In this article, we have answered some frequently asked questions about algebraic expressions, focusing on the process of solving them. We have discussed the importance of simplifying algebraic expressions, how to identify and combine like terms, and how to determine if an expression can be simplified further. By following these steps, we can simplify complex algebraic expressions and solve mathematical problems with ease.