Factorize each of the following expressions:
(a-3b)3+(3b-c)3+(c-a)3
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The algebraic expression is given as : (a - 3b)³ + (3b - c)³ + (c - a)³
Let (a - 3b) = a , (3b - c) = b , (c - a) = c. Then
a + b + c = a - 3b + 3b - c + c - a = 0
We know, a³ + b³ + c³− 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
∴ a³ + b³ + c³ = 3abc
⇒ (a - 3b)³ + (3b - c)³ + (c - a)³ = 3(a - 3b) (3b - c)(c - a)
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Answer:
Step-by-step explanation:
Let (a - 3b) = a , (3b - c) = b , (c - a) = c. Then
a + b + c = a - 3b + 3b - c + c - a = 0
We know, a³ + b³ + c³− 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)
∴ a³ + b³ + c³ = 3abc
⇒ (a - 3b)³ + (3b - c)³ + (c - a)³ = 3(a - 3b) (3b - c)(c - a)
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