The simplified answer is: " 10x² + 13x + 5 " .
_____________________________________________________
Explanation:
_____________________________________________________
Given:
_____________________________________________________
(7x²− 2x + 9) + (3x²+ 15x − 4) ;
→ Rewrite as: (7x²− 2x + 9) + 1(3x²+ 15x − 4)
___________________________________________
Considering the following portion of the expression:
___________________________________________
" 1(3x²+ 15x − 4) " ;
___________________________________________
Note the "distributive property of multiplication" :
___________________________________________
a(b + c) = ab + ac ;
a(b − c) = ab + ac ;
___________________________________________
Likewise:
a(b + c − d) = ab + ac − ad ;
___________________________________________
So; 1(3x²+ 15x − 4) = (1*3x²) + (1*15x) − (1*4) ;
= 3x² + 15x − 4
Bring down the: "(7x²− 2x + 9)" ; and rewrite the expression:
___________________________________________________
7x² − 2x + 9 + 3x² + 15x − 4 ;
Combine the "like terms" :
+7x² + 3x² = + 10x² ;
- 2x + 15x = + 13x ;
+ 9 − 4 = + 5 ;
____________________________________________________
and rewrite the expression:
____________________________________________________
which is: " 10x² + 13x + 5 " .
____________________________________________________
