Question

factorise =(a-b)³ + (b-c) ³ + ( c-a) ³​

Answer 1

Answer:

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

Explanation:

Answer 2

Hey friend!

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To Factorise (a - b)³ + (b - c)³ + (c - a)³

We will apply one algebraic identity over here,

(x - y)³ = x³ - 3xy(x - y) - y³

Now,

(a - b)³ + (b - c)³ + (c - a)³

→ a³ - 3ab(a - b) - b³ + b³ - 3bc(b - c) - c³ + c³ - 3ac(c - a) - a³

→ - 3ab(a - b) - 3bc(b - c) - 3ac(c - a)

→ - 3 [ab(a -  b) + bc(b - c) + ac(c - a)]

→ - 3 [a²b - ab² + b²c - bc² + ac² - a²c]

Answer: - 3 [a²b - ab² + b²c - bc² + ac² - a²c]

I hope it helps you and if you appreciate my answer, please respond with a thanks.