Consider the following pattern:

Using the above pattern, find the value of the following:
(i) $23^{3} - 22^{3}$
(ii) $30^{3} - 29^{3}$

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Solution

(i) $23^{3} - 22^{3}$
According to the pattern, we have,
$23^{3} - 22^{3} = 1 + 23 \times 22 \times 3$
$= 1519$ [1 Mark]

(i) $30^{3} - 29^{3}$
According to the pattern, we have,
$30^{3} - 29^{3} = 1 + 30 \times 29 \times 3$
$= 2611$ [1 Mark]

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