Toán Lớp 8: `(x-1)(x-3)(x-4)(x-5)+(x-3)(x-6)(x+8)+(x+18)(x+19)+(x-3)^3-(x-9)^3` Rút gọn nào =))

Question

Toán Lớp 8:  (x-1)(x-3)(x-4)(x-5)+(x-3)(x-6)(x+8)+(x+18)(x+19)+(x-3)^3-(x-9)^3 Rút gọn nào =))

cobebongdem · Answer

Giải đáp:     &darr;&darr;     Lời giải và giải thích chi tiết:      (x-1)(x-3)(x-4)(x-5)+(x-3)(x-6)(x+8)+(x+18)(x+19)+(x-3)&sup3;-(x-9)&sup3;   =(x&sup2;-4x+3)(x&sup2;-9x+20)+(x&sup2;-9x+18)(x+8)+x&sup2;+37x+342+(x-3-x+9)[(x-3)&sup2;+(x-3)(x-9)+(x-9)&sup2;]   =x⁴-9x&sup3;+20x&sup2;-4x&sup3;+36x&sup2;-80x+3x&sup2;-27x+60+x&sup3;+8x&sup2;-9x&sup2;-72x+18x+144+x&sup2;+37x+342+6.(3x&sup2;-36x+117) =x⁴-9x&sup3;+20x&sup2;-4x&sup3;+36x&sup2;-80x+3x&sup2;-27x+60+x&sup3;+8x&sup2;-9x&sup2;-72x+18x+144+x&sup2;+37x+342+18x&sup2;-216x+702   =x⁴+(-9x&sup3;-4x&sup3;+x&sup3;)+(20x&sup2;+36x&sup2;+3x&sup2;+8x&sup2;-9x&sup2;+x&sup2;+18x&sup2;)+(-80x-27x-72x+18x+37x-216x)+(60+144+342+702)   =x⁴-12x&sup3;+77x&sup2;-340x+1248

truongthanhhung · Answer

$ text{Giải đáp:}$    (x-1)(x-3)(x-4)(x-5)+(x-3)(x-6)(x+8)+(x+18)(x+19)+(x-3)&sup3;-(x-9)&sup3;   =(x&sup2;-4x+3)(x&sup2;-9x+20)+(x&sup2;-9x+18)(x+8)+x&sup2;+37x+342+(x-3-x+9)[(x-3)&sup2;+(x-3)(x-9)+(x-9)&sup2;]   =x⁴-9x&sup3;+20x&sup2;-4x&sup3;+36x&sup2;-80x+3x&sup2;-27x+60+x&sup3;+8x&sup2;-9x&sup2;-72x+18x+144+x&sup2;+37x+342+6.(3x&sup2;-36x+117)   =x⁴-9x&sup3;+20x&sup2;-4x&sup3;+36x&sup2;-80x+3x&sup2;-27x+60+x&sup3;+8x&sup2;-9x&sup2;-72x+18x+144+x&sup2;+37x+342+18x&sup2;-216x+702   =x⁴+(-9x&sup3;-4x&sup3;+x&sup3;)+(20x&sup2;+36x&sup2;+3x&sup2;+8x&sup2;-9x&sup2;+x&sup2;+18x&sup2;)+(-80x-27x-72x+18x+37x-216x)+(60+144+342+702)   =x⁴-12x&sup3;+77x&sup2;-340x+1248