Question

Verify the following:

(i) $18\times [9+(-7\left)\right]=18\times 9+18\times (-7)$

(ii) $(-13)\times \left[\right(-6)+(-19\left)\right]=(-13)\times (-6)+(-13)\times (-19)$

Answer 1

The given questions will follow distributive property for addition

i.e. $a\times (b+c)=a\times b+a\times c$

(i) $18\times [9+(-7\left)\right]=18\times 9+18\times (-7)$

​L.H.S. $=18\times [9+(–7\left)\right]$
$=18\times [9–7]$
$=18\times 2$
$=36$
R.H.S.$=18\times 9+18\times (–7)$

$=162–(18\times 7)$
$=162–126$
$=36$
$\therefore$ L.H.S = R.H.S
Hence, verified.
(ii) $(–13)\times \left[\right(–6)+(–19\left)\right]=(–13)\times (–6)+(–13)\times (–19)$
L.H.S. $=(–13)\times \left[\right(–6)+(–19\left)\right]$
$=(–13)\times [–6–19]$
$=(–13)\times (–25)$
$=325$
R.H.S.$=(–13)\times (–6)+(–13)\times (–19)$
$=78+247$
$=325$
$\therefore$ L.H.S = R.H.S
Hence, verified.