Using binomial theorm evaluate (101)(101)(101)

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Solution

$101 \times 101 \times 101 = 101^{3} = {(100 + 1)}^{3} =^{3} C_{0} 100^{3} \times 1^{0} +^{3} C_{1} 100^{2} \times 1^{1} +^{3} C_{2} 100^{1} \times 1^{2} +^{3} C_{3} 100^{0} \times 1^{3} = 1 \times 1000000 + 3 \times 10000 + 3 \times 100 + 1 = 1030301$

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