Question

Find the product $103\times 98$ by using special product.

Answer 1

We observe that
$103\times 98=(100+3)(100-2)$
$=(100{)}^2+(\left(3\right)+(-2))\times 100+(3\times (-2))$
$=10000+(1\times 100)+(-6)=10094$,
where we have taken $x=100,a=3$ and $b=2$ in the expansion: $(x+a)(x+b)=x^2+(a+b)x+ab$.