If (P)8 represents the number P in base - 8, then (144)8 + (175)8 =

First, convert both numbers from base -8 to decimal.

(144)_{-8} = 1(-8)^2 + 4(-8)^1 + 4(-8)^0 = 64 - 32 + 4 = 36

(175)_{-8} = 1(-8)^2 + 7(-8)^1 + 5(-8)^0 = 64 - 56 + 5 = 13

Add the decimal values: 36 + 13 = 49.

Convert 49 back to base -8: 49 ÷ (-8) = -6 remainder 1; -6 ÷ (-8) = 1 remainder 2; 1 ÷ (-8) = 0 remainder 1. Reading remainders bottom-up gives (121)_{-8}.