Разложить ** множители! (4-t)^3-t*(t-3)*(t+2)-64-t^2+2t

Question

Разложить на множители!
(4-t)^3-t*(t-3)*(t+2)-64-t^2+2t

Answer 1

Применяем способ группировки
(4-t)³-t·(t-3)·(t+2)-64-t²+2t=(4-t)³-64  - t·(t-3)·(t+2)-(t²-2t)=
=(4-t)³-4³  - t·(t-3)·(t+2)-(t²-2t)= (4-t-4)·((4-t)²+4(4-t)+16)- t·(t-3)·(t+2)-t·(t-2)=
=-t·(16-8t+t²+16-4t+16)-t·(t-3)·(t+2)-t·(t-2)=t(t²-12t+48)-t·(t²-t-6)-t·(t-2)=
=t·(t²-12t+48-t²+t+6-t+2)=t·(-12t+56)=-4t·(3t-14)