Factorise a minus b cube plus b minus c cube plus c minus a cube
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Step-by-step explanation:
=(a-b)^3+(b-c)^3+(c-a)^3
=a^3-3a^2b+3ab^2-b^3+b^3-3b^2c+3bc^2-c^3+c^3-3c^2a+3ca^2-a^3
=-3a^2b+3ab^2-3b^2c+3bc^2-3c^2a+3ca^2
=3ab(a-b)-3c(b^2-a^2)+3c^2(b-a)
=(b-a)(-3ab-3bc-3ac+3c^2)
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