Factorize the polynomial x^3+y^3+z^3−3xyz

Holetaug 2022-07-13 Answered
Factorize the polynomial x 3 + y 3 + z 3 3 x y z
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Answers (1)

Monserrat Cole
Answered 2022-07-14 Author has 12 answers
Solution:
x 3 + y 3 + z 3 3 x y z = x 3 + y 3 + 3 x 2 y + 3 x y 2 + z 3 3 x y z 3 x 2 y 3 x y 2 = ( x + y ) 3 + z 3 3 x y ( x + y + z ) = ( x + y + z ) ( ( x + y ) 2 + z 2 ( x + y ) z ) 3 x y ( x + y + z ) = ( x + y + z ) ( x 2 + 2 x y + y 2 + z 2 y z x z 3 x y ) = ( x + y + z ) ( x 2 + y 2 + z 2 x y y z z x )
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