Q1 of 34 Page 178

Take various positive and negative numbers as x, y, z and compute (x + y)z and xz + yz. Check whether the equation (x + y)z = xz + yz holds for all these.

let, take x = 0,1,-1 y = 1,0,-1 and z = -1,1,0 respectively.

CASE 1:When x = 0, y = 1, and z = -1,


(x + y)z = (0 + 1)-1


= 1×-1


= -1


CASE 2:When x = 1, y = 0, and z = 1,


(x + y)z = (1 + 0)1


= 1×1


= 1


CASE 3:When x = -1, y = -1, and z = 0,


(x + y)z = (-1-1)0


= -2×0


= 0


Calculating xz + yz


CASE 1:when x = 0, y = 1, and z = -1,


xz + yz = 0×-1 + 1×-1


= 0 - 1


= -1


CASE 2:When x = 1, y = 0 and z = 1,


xz + yz = 1×1 + 0×1


= 1 + 0


= 1


CASE 3: When x = -1, y = -1 and z = 0


Xz + yz = -1×0 + (-1×0)


= 0 + 0


= 0


As in all case (x + y)z = xz + yz hence, it will holds for all numbers.


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