If x^3+y^3=(100010111)₂ and x+y=(11111)₂ , then what is (x-y)^2+x y equal to?

Step-by-step solution

aligned & x^3+y^3=2^8+2^4+2^2+2^1+2^0 & =256+16+4+2+1=279 & x+y=2^4+2^3+2^2+2^1+2^0 & =16+8+4+2+1=31 aligned Now, (x-y)^2+x y= (x+y) [x^2-x y+y^2 ] x+y = x^3-y^3 x+y = 279 31 =9 array c|c|c 2 & 9 & 2 & 4 & 1 2 & 2 & 0 & 1 & 0 array 9=[1001]₂