Problem 47 Combine like terms. $$ 3 a b... [FREE SOLUTION]

Chapter 5: Problem 47

Combine like terms. $$ 3 a b^{2}+7 a^{2} b-5 a b^{2}+13 a^{2} b $$

Short Answer

Expert verified

-2ab^{2} + 20a^{2} b

Step by step solution

Identify Like Terms

Examine the terms in the expression and group the like terms. The like terms are those that have the same variables raised to the same powers. Here, the like terms are: 1. $3ab^{2} $ and $-5ab^{2}$2. $7a^{2} b$ and $13a^{2} b$

Combine Like Terms

Add or subtract the coefficients of the like terms: 1. $3ab^{2} - 5ab^{2} = (3 - 5)ab^{2} = -2ab^{2}$2. $7a^{2} b + 13a^{2} b = (7 + 13)a^{2} b = 20a^{2} b$

Write the Simplified Expression

Combine the results from the previous step to obtain the final simplified expression: $-2ab^{2} + 20a^{2} b$

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Key Concepts

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

like terms

In algebra, the concept of 'like terms' is crucial for simplifying expressions. Like terms are terms that have the same variables raised to the same powers. This means the coefficients (the numerical part) can be different, but the variable part must match exactly. Here are some examples to make it clearer:

For the terms $3ab^2$ and $-5ab^2$, the variable part $ab^2$ is the same, so these are like terms.
However, the terms $7a^2b$ and $13ab^2$ aren't like terms because their variable parts are different.

Grouping like terms is the first step in simplifying expressions. Look for terms with identical variable parts and then combine their coefficients.

coefficients

Coefficients are the numerical parts of terms that multiply the variables. When combining like terms, you only add or subtract the coefficients while keeping the variable part the same.

For instance, in $3ab^2$, the coefficient is 3, and in $-5ab^2$, the coefficient is -5. To combine these like terms, you'd perform the operation on the coefficients: \[3ab^2 - 5ab^2 = (3 - 5)ab^2 = -2ab^2\]
Similarly, for the terms $7a^2b$ and $13a^2b$, you'd combine the coefficients: \[7a^2b + 13a^2b = (7 + 13)a^2b = 20a^2b\]

Understanding coefficients makes it easier to manipulate and simplify algebraic expressions.

simplifying expressions

Simplifying expressions involves combining like terms to make the expression easier to work with. This process helps in solving equations and understanding the relationships between different variables.

Start by identifying like terms and their coefficients.
Perform the necessary addition or subtraction on the coefficients.
Maintain the same variable part while combining like terms.

For example, if you have the expression: \[3ab^2 + 7a^2b - 5ab^2 + 13a^2b\]First, identify the like terms:

$3ab^2$ and $-5ab^2$
$7a^2b$ and $13a^2b$

Next, combine them by adding or subtracting the coefficients:

$3ab^2 - 5ab^2 = -2ab^2$
$7a^2b + 13a^2b = 20a^2b$

Finally, write the simplified expression by combining the results:\[-2ab^2 + 20a^2b\]This simplification makes further calculations much easier.

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91影视

Combine like terms. $$ 3 a b^{2}+7 a^{2} b-5 a b^{2}+13 a^{2} b $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Write the Simplified Expression

Key Concepts

like terms

coefficients

simplifying expressions

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