Write in the expanded form-100-p3-q3-r3

100×p^3×q^3×r^3 = 100 × p× p× p× q× q× q× r× r× r ...

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Question

Write in the expanded form.
$100 \times p^{3} \times q^{3} \times r^{3}$

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

$\frac{p^{3} + q^{3} + r^{3}}{p^{2} q^{2} r^{2}} = \frac{1}{p^{3}} + \frac{1}{q^{3}} + \frac{1}{r^{3}}$

p^{3} {(q - r)}^{3} + q^{3} {(r - p)}^{3} + r^{3} {(p - q)}^{3}

p^{3} (q - r)^{3} + q^{3} (r - p)^{3} + r^{3} (p - q)^{3}

p^{3} (q - r)^{3} + q^{3} (r - p)^{3} + r^{3} (p - q)^{3}

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