x^3(y-x)^3 + y^3(z-y)^3 + z^3(x-y)^3 Factorize the following polynomial. Please show the steps as well. @moderators and @genius please help :)
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x^3(y-x)^3 + y^3(z-y)^3 + z^3(x-y)^3 Factorize the following polynomial. Please show the steps as well. @moderators and @genius please help :)
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Appropriate Question :-
Factorize the following :
Given that
can be rewritten as
Let assume that,
On adding above three equations, we get
We know,
If a + b + c = 0, then
Hence,
Therefore,
Additional Information :-
More Identities to know:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a + b)(a - b)
(a + b)² = (a - b)² + 4ab
(a - b)² = (a + b)² - 4ab
(a + b)² + (a - b)² = 2(a² + b²)
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
Answer:
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