Using binomial evaluate the following: (101)^4 - Vidyadip

Question

Using binomial evaluate the following:
$(101)^4$

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Answer

We have,
$(101)^4=(100+1)^4$
$={^4\text{C}}_0\times100^4+{^4\text{C}}_1\times100^3+{^4\text{C}}_2\times100^2+{^4\text{C}}_3\times100+{^4\text{C}}_4$
$=100^4+4\times100^3+6\times100^2+4\times100+1$
$=100000000+4000000+60000+400+1$
$=104060401$
$\therefore(101)^4=104060401$

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