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m^{3}-6m^{2}+12m-8-\left(m+1\right)^{3}-9\left(m-m^{2}-1\right)
\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(m-2\right)^{3} kengaytirilishi uchun ishlating.
m^{3}-6m^{2}+12m-8-\left(m^{3}+3m^{2}+3m+1\right)-9\left(m-m^{2}-1\right)
\left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} binom teoremasini \left(m+1\right)^{3} kengaytirilishi uchun ishlating.
m^{3}-6m^{2}+12m-8-m^{3}-3m^{2}-3m-1-9\left(m-m^{2}-1\right)
m^{3}+3m^{2}+3m+1 teskarisini topish uchun har birining teskarisini toping.
-6m^{2}+12m-8-3m^{2}-3m-1-9\left(m-m^{2}-1\right)
0 ni olish uchun m^{3} va -m^{3} ni birlashtirish.
-9m^{2}+12m-8-3m-1-9\left(m-m^{2}-1\right)
-9m^{2} ni olish uchun -6m^{2} va -3m^{2} ni birlashtirish.
-9m^{2}+9m-8-1-9\left(m-m^{2}-1\right)
9m ni olish uchun 12m va -3m ni birlashtirish.
-9m^{2}+9m-9-9\left(m-m^{2}-1\right)
-9 olish uchun -8 dan 1 ni ayirish.
-9m^{2}+9m-9-9m+9m^{2}+9
-9 ga m-m^{2}-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
-9m^{2}-9+9m^{2}+9
0 ni olish uchun 9m va -9m ni birlashtirish.
-9+9
0 ni olish uchun -9m^{2} va 9m^{2} ni birlashtirish.
0
0 olish uchun -9 va 9'ni qo'shing.