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Factorize each of the following expressions:$(a - 3b)^3 + (3b - c)^3 + (c - a)^3$
Given:
$(a - 3b)^3 + (3b - c)^3 + (c - a)^3$
To do:
We have to multiply the given expressions.
Solution:
We know that,
$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$
$a^3 + b^3 + c^3 = 3abc$ if $a + b + c = 0$
Here,
$a - 3b + 3b - c + c - a = 0$
Therefore,
$(a - 3b)^3 + (3b - c)^3 + (c - a)^3 = 3 (a - 3b) (3b - c) (c - a)$
Hence, $(a - 3b)^3 + (3b - c)^3 + (c - a)^3 = 3 (a - 3b) (3b - c) (c - a)$.
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