Question

p^3-27q^3+8r^3+18pqr





please answer fast

Answer 1

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Let p(q - r) = a, q(r - p) = b and r(p - q) = c, 

=> a + b + c = 0 

=> a + b = - c 

=> (a + b)³= - c³ 

=> a³ + b ³ + 3ab(a + b) + c³= 0 

=> a³ + b³ + c³ = 3abc (because a + b = - c) 

Now, p³(q – r)³+ q³(r – p)³ + r³(p – q)³ = 

a³+ b³+ ³

= 3abc 

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

Answer 2

Answer:

I think I have to factories this

Let p(q - r) = a, q(r - p) = b and r(p - q) = c, 

a + b + c = 0

 

a + b = - c 

(a + b)^3 = - c^3 

a^3 + b^3 + 3ab(a + b) + c^3 = 0 

a^3 + b^3 + c^3 = 3abc (because a + b -c) 

Now, p3(q – r)3 + q3(r – p)3 + r3(p – q)3 = a^3 + b^3 + c^ 

= 3abc 

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

JAI SHREE KRISHNA