Verify the following: 

(a) $18\times \left[7+(-3)]=[18\times 7]+[18\times (–3)\right]$ 

(b) $(-21)\times \left[(-4)+(-6)\right]=\left[(-21)\times (- 4)\right]+\left[(-21)\times (- 6)\right]$

(a)  Consider the given expression,  $18\times \left[7+(-3)]=[18\times 7]+[18\times (–3)\right]$.

First, consider the LHS to get the following

$=18\times \left[7+(–3)\right]$

$=18\times [7-3]$

$=18\times 4$

$=72$

Now, consider the RHS to get the following

$=[18\times 7]+[18\times (-3\left)\right]$

$=\left[126\right]+[-54]$

$=126–54$

$=72$

Therefore, 

$\mathrm{LHS}=\mathrm{RHS}$

Hence, the given expression is verified.