Simplify (7x^2− 2x + 9) + (3x^2+ 15x − 4).

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 " .