Question

Using identities, evaluate ${99}^2$

Answer 1

Compute the required value:

Given expression is ${99}^2$.

${99}^2$ can be written as ${\left(100-1\right)}^2$

$\begin{array}{crclc}\therefore & {\left(99\right)}^2& =& {\left(100-1\right)}^2& \\ & & =& {\left(100\right)}^2-2\left(100\right)\left(1\right)+1^2& \left[\because {\left(a-b\right)}^2=a^2-2\mathrm{ab}+b^2\right]\\ & & =& 10,000-200+1& \\ \Rightarrow & {\left(99\right)}^2& =& 9801& \end{array}$

Hence the required value is $9801$.