State True or False.
$(p - q)^{3} + (q - r)^{3} + (r - p)^{3} = 3 (p - q) (q - r) (r - p)$

True

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False

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Solution

The correct option is A True
$L . H . S . = (p - q)^{3} + (q - r)^{3} + (r - p)^{3}$
$= p^{3} - q^{3} - 3 p^{2} q + 3 p q^{2} + q^{3} - r^{3} - 3 q^{2} r + 3 q r^{2} + r^{3} - p^{3} - 3 r^{2} p + 3 r p^{2}$
$= 3 (p q^{2} - p^{2} q + q r^{2} - q^{2} r + r p^{2} - r^{2} p)$
$= 3 (p - q) (q - r) (r - p)$
$= R . H . S .$

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Similar questions

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

The factors of $(p - q)^{3} + (q - r)^{3} + (r - p)^{3}$ are:

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

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

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