Question

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

Answer 1

HELLO!

YOUR'S ANSWER :-

${x}^{3} + {y}^{3} + {z}^{3} \\ ( {x}^{2} + {y}^{2} + {z}^{2} - xy - yz - zx + 3xyz$

IF,

${x}^{3} + {y}^{3} + {z}^{3} = 3xz.........(1)$

ACCORDING TO THE PROBLEM

LET

$x = a - b \\ y = b - c \\ z = c - a \\ x + y + z = a - b + b - c + c - a = 0$

THEREFORE,

USING IDENTITY

${x}^{3} + {y}^{3} + {z}^{3} = 3xyz \\ {(a - b)}^{3} + {(b - c)}^{3} + {(c - a)}^{3} \\ 3(a - b)(b - c)(c - a)$

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