Observe the following pattern.
$2^{3}-1^{3}=1+2 \times 1 \times 3$
$3^{2}-2^{3}=1+3 \times 2 \times 3$
$4^{3}-3^{3}=1+4 \times 3 \times 3$
Using this pattern, find the value of each of the following.
$( a).\ 81^{3}-80^{3}$
$( b).\ 100^{3}-99^{3}$

To do: To find the value of each of the following, by using the given pattern:

$( a).\ 81^{3}-80^{3}$          $( b).\ 100^{3}-99^{3}$
 

Solution:

$( a).\ 81^{3}-80^{3}$

$=1+81\times80\times3$

$=1+19440$

$=19441$

$( b).\ 100^{3}-99^{3}$

$=1+100\times99\times3$

$=1+29700$

$=29701$

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Updated on: 10-Oct-2022

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