Subtract (7x^2 + 4x - 6) - (2x^2 - 3x + 1) me and show each step so ill understand

 The simplified expression is:  " 5x² + x – 7 " . 

Note:

We are given:


          →   " (7x² + 4x – 6) – (2x² – 3x + 1) "  ; 

Let us simplify this expression:

Rewrite as:


  (7x² + 4x – 6) – 1(2x² – 3x + 1) ; 

{Since there is an implied "one", since "1" ; multiplied by any value, results in the same value} ; 

Let us start with the following part of the expression:

        →        "  – 1(2x² – 3x + 1) "  ;

Note the "distributive property" of multiplication:

 a(b + c)  = ab + ac ;

 a(b – c) = ab – ac ;


As such:  " a(b – c + d) = ab – ac + ad "  ; 

So:

 →   " – 1(2x² – 3x + 1) " =  (-1 * 2x²)  – (-1* -3x)  + (-1 * 1) ; 

                                                   =  -2x²  – 3x + (-1) ; 

                                                  =   -2x²  –  3x  –  1 ;

Now, bring down the: " 7x² + 4x – 6 " ;  and add the " – 2x² –  3x  –  1 " ; 

as follows:

         →  "  7x² + 4x – 6 – 2x² –  3x  –  1  "  ;

         →  Combine the "like terms" :

               + 7x² – 2x²  = + 5x²  ;

               + 4x  –  3x  =  + 1x =  + x ; 

               – 6   –  1   =   – 7 ; 

And we can rewrite the simplified expression as:

        →   "  5x² + x – 7 " . 

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