Question

1)Completati , astfel incit propozitia obtinuta sa fie adevarata

36t²-...+4=(...-...)²

Descompuneti in factori

(x+1)³-(x-2)³

Answer 1

36t²-...+4=(...-...)²    Observam ca  √36t²=6t si √4=2   si le inmultim cu 2

36t²-(6x2x2)t+4=(6t-2)²     =>   36t²-24t+4=(6t-2)²

                                METODA  1   ( deschidem parantezele)

(x+1)³-(x-2)³=(x+1)²(x+1) - (x-2)²(x-2)=(x²+2x+1)(x+1) - (x²-4x+4)(x-2)

=> x³+2x²+x+x²+2x+1-x³+4x²-4x+2x²-8x+8=9x²-9x+9=9(x²-x+1)

                                  METODA 2        >   formula a³-b³=(a-b)(a²-ab+b²) <

  (x+1)³-(x-2)³=(x+1-x+2) ([x²+2x+1]-[x²-x-2]+[x²-4x+4])

=> 3(x²-x+7)=3x²-3x+21