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How do you combine like terms in $6m - 5m + \left( { - 8m} \right) + \left( { - m} \right) + \left( { - 10m} \right) + \left( { - 5m} \right)$?

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Last updated date: 22nd Jun 2024
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Answer
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Hint: This is a linear expression in one variable and all the terms have one variable $m$. First we have to solve the brackets. We know that the combination of two same signs will give positive and the combination of two opposite signs will give us negative sign while opening brackets. After opening the brackets, combine the positive terms and negative terms separately and find its value.

Complete step by step answer:
According to the question, we have to show the method to combine like terms in the given algebraic expression.
The algebraic expression is $6m - 5m + \left( { - 8m} \right) + \left( { - m} \right) + \left( { - 10m} \right) + \left( { - 5m} \right)$.
Let the value of this expression is $x$. Then we have:
$ \Rightarrow x = 6m - 5m + \left( { - 8m} \right) + \left( { - m} \right) + \left( { - 10m} \right) + \left( { - 5m} \right)$
First we will open the brackets. We know that the combination of two same signs will give positive and the combination of two opposite signs will give us negative sign while opening brackets. Applying this rule for the above expression, we’ll get:
$ \Rightarrow x = 6m - 5m - 8m - m - 10m - 5m$
As we can see that only the first term is positive and all the other terms are negative. Combining positive terms together and negative terms together and solving them separately, we‘ll get:
$
   \Rightarrow x = 6m - \left( {5m + 8m + m + 10m + 5m} \right) \\
   \Rightarrow x = 6m - 29m \\
   \Rightarrow x = - 23m \\
 $
Therefore the final value of the expression $6m - 5m + \left( { - 8m} \right) + \left( { - m} \right) + \left( { - 10m} \right) + \left( { - 5m} \right)$ is $ - 23m$. This is the method how we combine the like terms and find the values of such expressions.

Note: If in an algebraic expression:
(1) If the combination of variables in two terms is different then we can’t add or subtract their coefficient to bring it in one term. For example, $2x + 3y$ is the simplest form of this expression and we can’t add the coefficients of the two terms because they have different variables.
(2) If the variables are same in both the terms but the degree is different then also we can’t add or subtract their coefficients. For example, $4{x^2} + 7x$ is the simplest form of this expression and we can’t add the coefficients of the two terms because in the first term, the degree of variable is 2 but it 1 in the second term.