Question

(p-q)^3 + (q-r)^3 + (r-p)^3
FACTORIES​

Answer 1

Step-by-step explanation:

let,

• a = p - q
• b = q - r
• c = r - p

So, the given expression becomes,

a³ + b³ + c³

Now,

a + b + c = p - q + q - r + r - p = 0

So,

a + b + c = 0

Therefore,

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

Since (a + b + c) = 0,

So,

a³ + b³ + c³ - 3abc = 0

=> a³ + b³ + c³ = 3abc

Now, putting the values of a, b, c, We get,

(p - q)³ + (q - r)³ + (r - p)³ = 3(p - q)(q - r)(r - p)

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