Question

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

Answer 1

(i) $103\times 107$

$=(100+3)(100+7)$

$=(100{)}^2+(3+7\left)\right(100)+(3\left)\right(7)$

$=10000+1000+21=11021$

(ii) $95\times 96$

$=(90+5)(90+6)=(90{)}^2+(5+6\left)\right(90)+(5\left)\right(6)$

$=8100+990+30=9120$

(iii) $104\times 96$

$=(100+4)(100-4)$

$=(100{)}^2-(4{)}^2$

$=10000-16=9984$