Question

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

Answer 1

(i) $103\times 107=(100+3)(100+7)$
$=(100{)}^2+(3+7)\times 100+3\times 7$
$=10000+1000+21=11021$

(ii) $95\times 96=(100-5)(100-4)$
$=(100{)}^2-(5+4)\times 100+5\times 4$
$=10000-900+20=9120$

(iii) Using identity: $(a+b)(a-b)=a^2-b^2$
$\therefore 104\times 96$
$=(100+4)(100-4)$
$=({100}^2-4^2)$
$=10000-16=9984$