Question

Using$(x+a)(x+b)=x^2+(a+b)x+ab$, find $9.7x9.8$

Answer 1

Since, $9.7x9.8$ can be written as$(9+0.7)(9+0.8)$

So, using $(x+a)(x+b)=x^2+(a+b)x+ab$

and putting $x=9,a=0.7,b=0.8$, we get

$(9+0.7)(9+0.8)=9^2+(0.7+0.8)\times 9+(0.7\times 0.8)$

$\Rightarrow (9+0.7)(9+0.8)=81+(1.5\times 9)+0.56$

$\Rightarrow (9+0.7)(9+0.8)=81+13.5+0.56$

$\Rightarrow (9+0.7)(9+0.8)=95.06$

Hence,$9.7x9.8=95.06$