Question

(m+n)^7 сколько будет и как решить

Answer 1

(m+n)⁷=(m+n)²⁺²⁺³=(m+n)²(m+n)²(m+n)³=
=(m²+2mn+n²)(m²+2mn+n²)(m³+3m²n+3mn²+n³)=
=(m⁴+2m³n+m²n²+2m³n+4m²n²+2mn³+m²n²+2mn³+n⁴)(m³+3m²n+3mn²+n³)=
=(m⁴+4m³n+6m²n²+4mn³+n⁴)(m³+3m²n+3mn²+n³)=
=m⁷+4m⁶n+6m⁵n²+4m⁴n³+m³n⁴+3m⁶n+12m⁵n²+18m⁴n³+12m³n⁴+3m²n⁵+
+3m⁵n²+12m⁴n³+18m³n⁴+12m²n⁵+3mn⁶+m⁴n³+4m³n⁴+6m²n⁵+4mn⁶+n⁷=
=m⁷+7m⁶n+21m⁵n²+35m⁴n³+35m³n⁴+21m²n⁵+7mn⁶+n⁷