Answer: The simplified expression is:
_______________________________________________________
x² + 5x + 49 .
__________________________________________
Explanation:
___________________________________________________
Given: (x² − 5x + 2) + (x² + 4x + 5) − (x² − 6x −42) ;
_____________________________________________
Start with adding the first two terms:
______________________________________________
(x² − 5x + 2) + (x² + 4x + 5) =
x² − 5x + 2 + x² + 4x + 5 = ?
______________________________________________
Combine the "like terms" :
______________________________________________
x² + x² = 2x² ;
-5x + 4x = - x
+2 +5 = +7
__________________________________
Rewrite as:
__________________________
2x² − x + 7 ;
______________________
Now, rewrite the entire expression:
___________________________
2x² − x + 7 − (x² − 6x − 42);
___________________________
Distribute the negative:
___________________________
Rewrite as:
___________________________
2x² − x + 7 − 1(x² − 6x − 42) ;
_____________________________
Let us consider:
_______________________________
-1(x² − 6x − 42) = -1x² + 6x + 42 ;
_________________________________
and rewrite the entire expression:
_________________________________
2x² − x + 7 − x² + 6x + 42 ;
_________________________________
Now, combine the "like terms" ; and simplify:
__________________________________________________________
+2x² - x² = x² ;
-x + 6x = + 5x ;
+7 + 42 = + 49
__________________________________________________________
We have: x² + 5x + 49 .
__________________________________________________________
