Sin 30 * cos 60 - cos^2 120 +sin 135 * cos 90

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To solve this, we will first find the values of the trigonometric functions at each angle:

sin 30 = 1/2
cos 60 = 1/2
cos 120 = -1/2
sin 135 = sqrt(2)/2
cos 90 = 0

Now we can substitute these values into the expression:

(1/2)(1/2) - (-1/2)^2 + (sqrt(2)/2)(0)
= 1/4 - 1/4 + 0
= 0

Therefore, the value of the expression sin 30 cos 60 - cos^2 120 + sin 135 cos 90 is 0.