Factroise x³-2√2y³+3√3z³ +3√6xyz
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Given : x³ - 2√2y³ + 3√3z³ + 3√6 xyz
To Find : Factorize
Solution:
x³ - 2√2y³ + 3√3z³ + 3√6 xyz
= x³ + ( -√2 y)³ + (√3 z)³ - 3 x(-√2 y) (√3z)
x = a
-√2 y = b
√3z = c
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ac)
= ( x - √2y + √3z) ( x² + 2y² + 3z² + √2xy + √6yz - √3xz)
x³ - 2√2y³ + 3√3z³ + 3√6 xyz =
( x - √2y + √3z) ( x² + 2y² + 3z² + √2xy + √6yz - √3xz)
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