Expand the given expression:(1/3x - 1/4y - 1/6z)2

1.	Expand the given expression:(1/3x - 1/4y - 1/6z)2
Answer» Given polynomial (1/3x - 1/4y - 1/6z)² represents identity (a + b + c)2, Where a = -1/3x, b = -1/4y and c = -1/6z Now apply values of a, b and c on the identity i.e. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca and we get: (1/3x - 1/4y - 1/6z)² = (-1/3x)² + (-1/4y)² + (-1/6z)² + 2(-1/3x)(-1/4y) + 2(-1/4y)(-1/6z) + 2(-1/6z)(-1/3x) Expand the exponential forms and we get: = 1/9x² + 1/16y² + 1/36z² + 2(-1/3x)(-1/4y) + 2(-1/4y)(-1/6z) + 2(-1/6z)(-1/3x) Solve multiplication process and we get: = 1/9x² + 1/16y² + 1/36z² + 1/6xy + 1/12yz + 1/9zx Hence, (1/3x - 1/4y - 1/6z)² = 1/9x² + 1/16y² + 1/36z² + 1/6xy + 1/12yz + 1/9zx

Answer»

Given polynomial (1/3x - 1/4y - 1/6z)² represents identity (a + b + c)2, Where a = -1/3x, b = -1/4y and c = -1/6z

Now apply values of a, b and c on the identity i.e. (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca and we get:

(1/3x - 1/4y - 1/6z)² = (-1/3x)² + (-1/4y)² + (-1/6z)² + 2(-1/3x)(-1/4y) + 2(-1/4y)(-1/6z) + 2(-1/6z)(-1/3x)

Expand the exponential forms and we get:

= 1/9x² + 1/16y² + 1/36z² + 2(-1/3x)(-1/4y) + 2(-1/4y)(-1/6z) + 2(-1/6z)(-1/3x)

Solve multiplication process and we get:

= 1/9x² + 1/16y² + 1/36z² + 1/6xy + 1/12yz + 1/9zx

Hence, (1/3x - 1/4y - 1/6z)² = 1/9x² + 1/16y² + 1/36z² + 1/6xy + 1/12yz + 1/9zx

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