What is the simplified form of the expression? -(8d - 3w) question 10 options: -8d + 3w 8d + 3w -8d - 3w 8d - 3w

The correct answer is:  [A]:  " - 8d + 3 " .

Explanation: 

Note the "distributive property" of multiplication:

     a(b + c) = ab +  ac ; 
  
     a(b − c) = ab − ac .


We are given the expression: 

  "  - (8d − 3w) " ; and are asked for the simplified expression; 

Consider this as:

 "  -1 (8d − 3w) " ;  

The "1" (in this case, "-1" ; since the "negative" sign is already present; is "implied" ; since any value, multiplied by "1", results in that very same value. 

So, using the "distributive property of multiplication" ; as explained above ;

       →   "  -1 (8d − 3w)  =  (-1 * 8d) − (-1 * 3w) ; 
 
                                      =  - 8d − (-3w) ;

                                      =  - 8d + 3w ;   → {since "subtracting a negative" is the 
                                                          same thing as "adding a positive"}; 

This answer corresponds to:  "Answer choice:  [A]:  " - 8d + 3w " . 


An additional note of interest: 

       Another simplified form of the expression would be:  " 3w − 8d " ;
HOWEVER, this is NOT among ANY of the answer choices given.

Note:  Consider our answer choice:  " [A]:  " - 8d + 3w " ; 

Note:  " - 8d  +  3w  =  3w  +  (- 8d) =  " 3w − 8d " ;  
    
                                                  →  {since "adding a negative" is the same as                                                                  "subtracting a positive" .}.

So;  note that:    

              →     "   - (x − y) = (y − x)   "  .

The main idea exclaims how everyone has mercy, even the greatest of kings yet have mercy.