Calculati (calcul algebric) :
a. (2x+1) * (2x-1) - (2x+1) * (2x+1) = ?
b. (x-2) * (x-3) - (x-1) * (x-5) = ?
c. (x-1) * (x-3) - (x-2) la puterea a -doua = ?
d. (x+2) *  -x+3) - (x+1) * ( +2x-5) = ?

p.s: vreau rezolvari cat mai detaliate, va rog! 

Răspuns :

       
         2                2
a) 4x      - 4x - 4x  + 2x + 2x + 1 = 1

b) x+ 6 + 4x + 5 = 5x+ 11
       2                    2
c) x - 3x - x + 3 - x - 4 = 2x-1
(2x+1) * (2x-1) - (2x+1) * (2x+1)=(2x+1)(2x-1-2x-1)=(2x+1)(-2)=-4x-2
(x-2) * (x-3) - (x-1) * (x-5)=(x^2-5x+6)-(x^2-6x+5)=x^2-5x+6-x^2+6x-5=x+1
(x-1) * (x-3) - (x-2)^2=(x^2-4x+3)-(x^2-4x+4)=x^2-4x+3-x^2+4x-4=-1

(x+2) * ( -x+3) - (x+1) * ( +2x-5)=(-x^2+x+6)-(2x^2-3x-5)=-x^2+x+6-2x^2+3x+5=
=-3x^2+4x+11