Evaluate the value of ${\left(101\right)}^2$by using suitable identity

$(101{)}^2$

$=(100+1{)}^2$

Using $(a+b{)}^2=a^2+b^2+2ab$

$(100+1{)}^2=100^2+1^2+2\times 100\times 1$

$=10000+1+200$

$=10000+201$

$=10201$.