Question

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

Answer 1

$$\begin{gathered} 101\times 101\times 101 \\ ={101}^3 \\ ={\left(100+1\right)}^3 \\ {=}^3{\mathrm{C}}_0{100}^3\times 1^0{+}^3{\mathrm{C}}_1{100}^2\times 1^1{+}^3{\mathrm{C}}_2{100}^1\times 1^2{+}^3{\mathrm{C}}_3{100}^0\times 1^3 \\ =1\times 1000000+3\times 10000+3\times 100+1 \\ =1030301 \end{gathered}$$