Question

Using a suitable identity evaluate ${\left(105\right)}^2$

Answer 1

$(105{)}^2=(100+5{)}^2$ $\left[\right(a+b{)}^2=a^2+b^2-2ab]$

$=(100{)}^2+(5{)}^2+2\left(5\right)\left(100\right)$

$=10000+25+1000$

$=11025$.