Question

Expand ${\left(99\right)}^2$ using suitable identities.

Answer 1

${\left(99\right)}^2={(100-1)}^2$

${(100-1)}^2$ is of the form ${(a-b)}^2=a^2+b^2-2ab$ where $a=100,b=1$

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

$=10000+1-200=10000-199=9801$