$6m - 9n + 27nx - 74mx =$
Answer (1)
Group the terms with common variables: ( 6 m − 74 m x ) + ( − 9 n + 27 n x ) .
Factor out common factors from each group: m ( 6 − 74 x ) + n ( − 9 + 27 x ) .
Rearrange terms within the parentheses: m ( 6 − 74 x ) + n ( 27 x − 9 ) .
Factor out constants from the parentheses where possible: 2 m ( 3 − 37 x ) + 9 n ( 3 x − 1 ) .
The simplified expression is: 2 m ( 3 − 37 x ) + 9 n ( 3 x − 1 ) .
Explanation
Understanding the Expression We are given the expression 6 m − 9 n + 27 n x − 74 m x and our goal is to simplify it by combining like terms and factoring.
Grouping Like Terms First, let's group the terms with common variables: ( 6 m − 74 m x ) + ( − 9 n + 27 n x ) This step helps us to identify common factors within each group.
Factoring Out Common Factors Next, we factor out the common factors from each group: m ( 6 − 74 x ) + n ( − 9 + 27 x ) This isolates the variable terms and constant terms.
Rearranging Terms Rearrange the terms within the parentheses to make the expression more readable: m ( 6 − 74 x ) + n ( 27 x − 9 ) This step is for aesthetic purposes and to prepare for further factoring.
Factoring Out Constants Now, let's factor out constants from the parentheses where possible: 2 m ( 3 − 37 x ) + 9 n ( 3 x − 1 ) This simplifies the expression further by extracting the greatest common factor from the constants.
Final Simplified Expression Finally, we check if further simplification or factoring is possible. In this case, no further simplification is apparent. Therefore, the simplified expression is: 2 m ( 3 − 37 x ) + 9 n ( 3 x − 1 )
Examples
In real life, simplifying algebraic expressions like this can be useful in various scenarios. For example, if you are calculating the cost of materials for a project, where m and n represent the quantities of two different materials and x represents a discount rate, simplifying the expression can help you quickly determine the total cost. Similarly, in physics, if m and n represent masses and x represents a variable affecting force, simplifying the expression can make calculations easier.
