Question

How do you simplify $0.028{m^7}n + 0.0327m{n^7} - 0.03{m^7}n - 0.046m{n^7}?$

Answer 1

Hint: To simplify the given expression, firstly with the help of commutative property of addition, group the similar terms that is all similar variables in a group or parentheses and constants in other group then perform the algebraic operation the expression has and finally see if there is any common factor between the terms of the expression if yes then take out the common factor and if no then congratulations you have simplified the expression.

Complete step-by-step solution:
In order to simplify the given expression $0.028{m^7}n + 0.0327m{n^7} - 0.03{m^7}n - 0.046m{n^7}$, we will first use the commutative property of addition to group similar terms in the expression as follows
$ = 0.028{m^7}n + 0.0327m{n^7} - 0.03{m^7}n - 0.046m{n^7}$
We can write this expression as
$ = 0.028{m^7}n + 0.0327m{n^7} + \left( { - 0.03{m^7}n} \right) + \left( { - 0.046m{n^7}} \right)$
Now, we can use commutative property of addition here in the above equation as follows
$
   = \left[ {0.028{m^7}n + \left( { - 0.03{m^7}n} \right)} \right] + \left[ {0.0327m{n^7} + \left( { - 0.046m{n^7}} \right)} \right] \\
   = \left[ {0.028{m^7}n - 0.03{m^7}n} \right] + \left[ {0.0327m{n^7} - 0.046m{n^7}} \right] \\
 $
Simplifying it further by doing the algebraic operations between similar terms, that is subtraction, we will get
\[ = - 0.002{m^7}n - 0.0133m{n^7}\]
Here in the above expression, we will check for any common factor between all terms of the expression
We can see that in both the terms of the above expression $( - mn)$ is a common factor, so taking it out as the common factor, we will get
\[ = - mn\left( {0.002{m^6} + 0.0133{n^6}} \right)\]
Therefore \[ - mn\left( {0.002{m^6} + 0.0133{n^6}} \right)\] is the simplified form of the given expression.

Note: We have written $ - 0.03{m^7}n\;{\text{and}}\; - 0.046m{n^7}\;{\text{as}}\; + \left( { - 0.03{m^7}n} \right)\;{\text{and}}\; + \left( { - 0.046m{n^7}} \right)$ because in order to use commutative property. This property holds true only for addition and multiplication operation, so we have changed the above subtraction into addition of negative numbers or variables to use commutative property. And in order to use commutative property for division, we convert it into multiplication with fraction.