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

Open in App

Solution

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

$a = p - q, b = q - r, c = r - p$

$∵ a + b + c = 0$ $a^{3} + b^{3} + c^{3} = 3 a b c$ (Identify)

$(p - q), (q - r), (r - p)$ factors

Suggest Corrections

Similar questions

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

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

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

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

I f p = 15, q = - 8, r = - 7, p^{3} + q^{3} + r^{3} =

Join BYJU'S Learning Program