By using binomial theorem, expand the following:
${(101)}^{4}$

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Solution

${(101)}^{4} = (100 + 1)^{4}$

Using binomial theorem, we have

$(100 + 1)^{4} = 4_{C_{0}} (100)^{4} + 4_{C_{1}} (100)^{3} (1) + 4_{C_{2}} (100)^{2} (1)^{2} + 4_{C_{3}} (100) (1)^{3} + 4_{C_{4}} (1)^{4}$

$= (100)^{4} + 4 (100)^{3} + 6 (100)^{2} + 4 (100) + 1$

$= 100000000 + 4000000 + 60000 + 400 + 1$

$= 104060401$

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