Question

3
s) Factorise: a3 (b-c)3 + b3(c-a) 3+ c3(a-b)3.
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Answer 1

Answer:

Here is your answer , I hope it will help you

Answer 2

Given

a³(b + c)³ + b³(c - a)³ + c³ (a - b)³

To find,

Factorised answer

Solution,

Since (a + b + c) = 0,

a³ + b³ + c³ = 3abc

Using this in the equation,

a(b - c) + b(c - a) + c(a - b)

= ab - ac + bc - ba + ca - cb

= ab - ba - ac + ca + bc - cb

= 0

So,

a³(b + c)³ + b³(c - a)³ + c³ (a - b)³

= {a (b - c)}³ + {b (c - a)}³ + {c (a - b)}³

= 3a(b - c)b(c - a)c(a - b)

= 3abc(a - b)(b - c)(c - a)

So, after factorising a³(b + c)³ + b³(c - a)³ + c³ (a - b)³ we get 3abc(a - b)(b - c)(c - a)