Problem 48 Combine like terms. $$ 6 m^{... [FREE SOLUTION]

Chapter 5: Problem 48

Combine like terms. $$ 6 m^{2} n-8 m n^{2}+3 m n^{2}-7 m^{2} n $$

Short Answer

Expert verified

-$m^{2}n - 5mn^{2} $

Step by step solution

Identify like terms

Recognize terms that have the same variables raised to the same powers. Here we have two sets of like terms: the terms containing $ m^{2}n $ and the terms containing $ mn^{2} $ .

Combine terms with $ m^{2}n $

Add or subtract the coefficients of the like terms with $ m^{2}n $. The terms are 6 $ m^{2}n $ and -7 $ m^{2}n $.\[6m^{2}n - 7m^{2}n = -1m^{2}n \]

Combine terms with $ mn^{2} $

Add or subtract the coefficients of the like terms with $ mn^{2} $. The terms are -8 $ mn^{2} $ and 3 $ mn^{2} $.\[ -8mn^{2} + 3mn^{2} = -5mn^{2} \]

Write the simplified expression

Combine the simplified groups from steps 2 and 3 to write the final answer.\[ -1m^{2}n - 5mn^{2} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms

In algebra, 'like terms' are terms that have the exact same variables raised to the same powers. For instance, in the expression 6$m^{2}n$-8$mn^{2}$+3$mn^{2}$-7$m^{2}n$, 6$m^{2}n$ and -7$m^{2}n$ are like terms because they both contain $m^{2}n$. Similarly, -8$mn^{2}$ and 3$mn^{2}$ are like terms because they both contain $mn^{2}$. Identifying like terms is essential because it allows us to combine them and simplify the expression.

Coefficients

Coefficients are the numerical parts of terms that multiply the variables. For example, in the term 6$m^{2}n$, the coefficient is 6. In -8$mn^{2}$, the coefficient is -8. To combine like terms, you add or subtract their coefficients while keeping the variable part unchanged.
For example:

6$m^{2}n$ - 7$m^{2}n$ becomes (-1)$m^{2}n$
-8$mn^{2}$ + 3$mn^{2}$ becomes -5$mn^{2}$

Remember, coefficients can be any real number, including negatives and fractions.

Algebraic Expression Simplification

Simplifying an algebraic expression involves combining like terms to make the expression easier to work with. Here鈥檚 a step-by-step breakdown of the process:

**Step 1: Identify like terms.** In our example: 6$m^{2}n$, -7$m^{2}n$, -8$mn^{2}$, and 3$mn^{2}$.
**Step 2: Combine the like terms with $m^{2}n$.** Add the coefficients of 6 and -7 to get (-1)$m^{2}n$.
**Step 3: Combine the like terms with $mn^{2}$.** Add the coefficients of -8 and 3 to get -5$mn^{2}$.
**Step 4: Write the simplified expression.** Combine the results from Steps 2 and 3 to get the final expression, which is -1$m^{2} n$ - 5$mn^{2}$.

By doing these steps, you make the original complex expression more manageable and easier to interpret and use in further calculations.

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91影视

Combine like terms. $$ 6 m^{2} n-8 m n^{2}+3 m n^{2}-7 m^{2} n $$

Short Answer

Step by step solution

Identify like terms

Combine terms with \( m^{2}n \)

Combine terms with \( mn^{2} \)

Write the simplified expression

Key Concepts

Like Terms

Coefficients

Algebraic Expression Simplification

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