Question

Using distributive law, find the square of $101$.

Answer 1

To find : the square of $101$ by using distributive law

On applying the distributive law, we obtain

We know that $101$ can be expressed as

$101=100+1$

So,

$$\begin{gathered} {101}^2={(100+1)}^2 \\ =(100+1)(100+1) \\ =100(100+1)+1(100+1) \\ =\left(\right(100\times 100)+(100\times 1\left)\right)+\left(\right(1\times 100)+(1\times 1\left)\right) \\ =10000+100+100+1 \\ =10201 \end{gathered}$$

Thus, the square of the given number i.e. ${101}^2=10201$