Question

Evaluate $102\times 98$ using suitable standard identity.

Answer 1

Using the identity $(x+a)(x+b)$ = $x^2+(a+b)x+ab$
Writing $102$ as $100+2$ and $98$ as $100-2$
Hence $(100+2)(100-2)$ = ${100}^2+[2+(-2\left)\right]100+\left(2\right)(-2)$
$=$ $10000+\left(0\right)100-4$
$=$ $9996$
The answer is $9996$