Factorise. (a-b)^3+(b-c)^3+(c-a)^3
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Answer:
a³-b³+b³-c³+c³-a³
A is cancelled by a
B is cancelled by b
C is cancelled by c
1
Hope it helps you
Step-by-step explanation:
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Given that: (a-b)^3+(b-c)^3+(c-a)^3
Using Property-
x^3+y^3+z^3-3xyz [Here, x=a-b, y=b-c, z=c-a]
As x+y+z=0,
x^3+y^3+z^3=3xyz
x^3+y^3+z^3= 3(a-b)(b-c)(c-a)
Hence, when factorised, we get-
a(b^2)-(a^2)b+b(c^2)-(b^2)c+c(a^2)-(c^2)a
Using Property-
x^3+y^3+z^3-3xyz [Here, x=a-b, y=b-c, z=c-a]
As x+y+z=0,
x^3+y^3+z^3=3xyz
x^3+y^3+z^3= 3(a-b)(b-c)(c-a)
Hence, when factorised, we get-
a(b^2)-(a^2)b+b(c^2)-(b^2)c+c(a^2)-(c^2)a
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