Question

Using identities, evaluate ${102}^2$.

Answer 1

Step 1: Write $102$ as a sum of two numbers

To Evaluate :${102}^2$

${102}^2$ can be written as ${(100+2)}^2$

${102}^2={(100+2)}^2$

Step 2: Use the identity ${(a+b)}^2=a^2+b^2+2ab$

Using the identity

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

$\begin{array}{rcl}{102}^2& =& {(100+2)}^2{(100+2)}^2={100}^2+2^2+2\times 100\times 2\\ {(100+2)}^2& =& {100}^2+2^2+400\\ {(100+2)}^2& =& 10000+400+4\\ {(100+2)}^2& =& 10404\\ \therefore {102}^2& =& 10404\end{array}$

Hence,${102}^2=10404$.