Solve (a+b)^100

$$( a + b ) ^ { 100 }$$

Expand

$$a^{100}+98913082887808032681188722800a^{49}b^{51}+93206558875049876949581681100a^{48}b^{52}+84413487283064039501507937600a^{47}b^{53}+73470998190814997343905056800a^{46}b^{54}+61448471214136179596720592960a^{45}b^{55}+49378235797073715747364762200a^{44}b^{56}+38116532895986727945334202400a^{43}b^{57}+28258808871162574166368460400a^{42}b^{58}+20116440213369968050635175200a^{41}b^{59}+13746234145802811501267369720a^{40}b^{60}+9013924030034630492634340800a^{39}b^{61}+5670048986634686922786117600a^{38}b^{62}+3420029547493938143902737600a^{37}b^{63}+1977204582144932989443770175a^{36}b^{64}+1095067153187962886461165020a^{35}b^{65}+580717429720889409486981450a^{34}b^{66}+294692427022540894366527900a^{33}b^{67}+143012501349174257560226775a^{32}b^{68}+66324638306863423796047200a^{31}b^{69}+29372339821610944823963760a^{30}b^{70}+12410847811948286545336800a^{29}b^{71}+4998813702034726525205100a^{28}b^{72}+1917353200780443050763600a^{27}b^{73}+699574816500972464467800a^{26}b^{74}+242519269720337121015504a^{25}b^{75}+79776075565900368755100a^{24}b^{76}+24865270306254660391200a^{23}b^{77}+7332066885177656269200a^{22}b^{78}+2041841411062132125600a^{21}b^{79}+535983370403809682970a^{20}b^{80}+132341572939212267400a^{19}b^{81}+30664510802988208300a^{18}b^{82}+6650134872937201800a^{17}b^{83}+1345860629046814650a^{16}b^{84}+253338471349988640a^{15}b^{85}+44186942677323600a^{14}b^{86}+7110542499799200a^{13}b^{87}+1050421051106700a^{12}b^{88}[phone]a^{11}b^{89}[phone]a^{10}b^{90}[phone]a^{9}b^{91}[phone]a^{8}b^{92}[phone]a^{7}b^{93}[phone]a^{6}b^{94}[phone]a^{5}b^{95}+3921225a^{4}b^{96}+161700a^{3}b^{97}+4950a^{2}b^{98}+100ab^{99}+b^{100}+98913082887808032681188722800b^{49}a^{51}+93206558875049876949581681100b^{48}a^{52}+84413487283064039501507937600b^{47}a^{53}+73470998190814997343905056800b^{46}a^{54}+61448471214136179596720592960b^{45}a^{55}+49378235797073715747364762200b^{44}a^{56}+38116532895986727945334202400b^{43}a^{57}+28258808871162574166368460400b^{42}a^{58}+20116440213369968050635175200b^{41}a^{59}+13746234145802811501267369720b^{40}a^{60}+9013924030034630492634340800b^{39}a^{61}+5670048986634686922786117600b^{38}a^{62}+3420029547493938143902737600b^{37}a^{63}+1977204582144932989443770175b^{36}a^{64}+1095067153187962886461165020b^{35}a^{65}+580717429720889409486981450b^{34}a^{66}+294692427022540894366527900b^{33}a^{67}+143012501349174257560226775b^{32}a^{68}+66324638306863423796047200b^{31}a^{69}+29372339821610944823963760b^{30}a^{70}+12410847811948286545336800b^{29}a^{71}+4998813702034726525205100b^{28}a^{72}+1917353200780443050763600b^{27}a^{73}+699574816500972464467800b^{26}a^{74}+242519269720337121015504b^{25}a^{75}+79776075565900368755100b^{24}a^{76}+24865270306254660391200b^{23}a^{77}+7332066885177656269200b^{22}a^{78}+2041841411062132125600b^{21}a^{79}+535983370403809682970b^{20}a^{80}+132341572939212267400b^{19}a^{81}+30664510802988208300b^{18}a^{82}+6650134872937201800b^{17}a^{83}+1345860629046814650b^{16}a^{84}+253338471349988640b^{15}a^{85}+44186942677323600b^{14}a^{86}+7110542499799200b^{13}a^{87}+1050421051106700b^{12}a^{88}[phone]b^{11}a^{89}[phone]b^{10}a^{90}[phone]b^{9}a^{91}[phone]b^{8}a^{92}[phone]b^{7}a^{93}[phone]b^{6}a^{94}[phone]b^{5}a^{95}+3921225b^{4}a^{96}+161700b^{3}a^{97}+4950b^{2}a^{98}+100ba^{99}+100891344545564193334812497256\left(ab\right)^{50}$$

Evaluate

$$\left(a+b\right)^{100}$$