Question

Evaluate the following products without multiplying directly: (i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96

Answer 1

1)103×107=(100+3)(100+7)
=(100)^2+(3+7)100+3*7
=10000+1000+21
=11021
2)95×96=(90+5)(90+6)
=(90)^2+(5+6)90+5×6
=8100+990+30
=9120
3)104*96=(100+4)(100-4)=100^2-4^2

=10000-16
=9984

Answer 2

$\bold{Hello \ friends}$

1. (100+ 3)(100+7) [ Writing 103 as 100+3 and 107 as 100+7]

=(100) square +(3+7)100+3×7

=10000+10×1000+21

11021

(by using this identity (x+a)(x+b)