If $p = 4$ , $q = - 3$ and $r = 2$ , find the value of :
$p^{3} + q^{3} - r^{3} - 3 p q r$

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Solution

Finding the value of the expression:
We have to find the value of expression $p^{3} + q^{3} - r^{3} - 3 p q r$ at $p = 4$ , $q = - 3$ and $r = 2$
Substituting $p = 4$ , $q = - 3$ and $r = 2$ in the given expression , we get
$p^{3} + q^{3} - r^{3} - 3 p q r = {(4)}^{3} + {(- 3)}^{3} - {(2)}^{3} - 3 \times 4 \times (- 3) \times 2 = 64 - 27 - 8 + 72 = 136 - 35 = 101$
Hence,the value of given expression will be $101$ .

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If q is the mean proportional between p and r prove that :

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