Using binomial evaluate the following: (102)^5 - Vidyadip

Question

Using binomial evaluate the following:
$(102)^5$

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Answer

We have,
$(102)^5=(100+2)^5$
$={^5\text{C}}_0\times100^5+{^5\text{C}}_1\times100^4\times2+{^5\text{C}}_2\times100^3\times2^2\\+{^5\text{C}}_3\times100^2\times2^3+{^5\text{C}}_4\times100\times2^4+{^5\text{C}}_5\times2^5$
$=100^5+5\times100^4\times2+10\times100^3\times2^2\\+10\times100^2\times2^3+5\times100\times2^4+2^5$
$=10000000000+1000000000+40000000+800000+8000+32$
$=11040808032$
$\therefore(102)^5=11040808032$

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