Using binomial theorem, evaluate: (102)^5 - Vidyadip

Question

Using binomial theorem, evaluate: $(102)^5$

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Answer

$(102)^5=(100+2)^5$
Using binomial theorem, we have
$(100+2)^5={ }^5 C_0(100)^5+{ }^5 C_1(100)^4(2)+{ }^5 C_2(100)^3(2)^2$
$+{ }^5 C_3(100)^2(2)^3+{ }^5 C_4(100)(2)^4+{ }^5 C_5(2)^5$
$=(100)^5+5(100)^4(2)+10(100)^3(2)^2+10(100)^2(2)^3+5(100)(2)^4+(2)^5$
$=10000000000+1000000000+40000000+800000+8000+32$
$=11040808032$

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