[tex]\displaystyle{ E(x) = (3x+2)^{2} -(2-3x)^{2} +(x-4)(2x-1) -2(x+6)^{2}+10(x+7) }[/tex]
[tex]\displaystyle{ E(x) = 9x^{2} + 12x + 4 - (4 -12x +9x^{2})+2x^{2}-x-8x+4 - 2\cdot (x^{2} + 12x + 36) + 10x + 70 }[/tex]
[tex]\displaystyle{ E(x) = 9x^{2}+12x+4-4+12x-9x^{2} + 2x^{2}-9x+4-2x^{2}-24x-72+10x+70 }[/tex]
[tex]\displaystyle{ E(x) = 12x + 12x + 2x^{2}-9x + 4 - 2x^{2} -14x -2 }[/tex]
[tex]\displaystyle{ E(x) = 24x - 23x -2 + 4 }[/tex]
[tex]\displaystyle{ E(x) = x + 2, \ \forall \ x \in \mathbb{R} }[/tex]
(QED)
[tex]\displaystyle{ S= E(1) + E(2) + ... + E(25)}[/tex]
[tex]\displaystyle{ S = (1 + 2) + (2+2) + .... + (25 + 2) }[/tex]
[tex]S = 3 + 4 + .... + 27[/tex]
Nr termeni = 27 - 3 + 1 = 24 + 1 = 25
[tex]\displaystyle{ S = (27 + 3) \cdot 25 : 2 }[/tex]
[tex]S = 30 : 2 \cdot 25[/tex]
[tex]S = 15 \cdot 25[/tex]
S = 375
