Concept:Formulaex3 + y3 = (x + y)(x2 - xy + y2)(x - y)2 = x2 - 2xy + y2Binary to decimal conversion formulaN = bn-1 × 2n-1 + b4 × 24 + b3 × 23 + b2 × 22 + b1 × 21 + b0 × 20 Where N is decimal equivalent, b is the binary digit, 2 is the base valueDecimal to Binary conversionStep 1: Divide the decimal number n by 2. Use the integer quotient obtained in this step as the dividend for the next step.Step 2: Write the remainder from bottom to top i.e. in the reverse chronological order.Calculation:Given:x3 + y3 = (100010111)2 and x + y = (11111)2Converting (100010111)2 to decimal form, we get,x3 + y3 = (100010111)2 = 1 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20 ? x3 + y3 = 256 + 16 + 4 + 2 + 1 ? x3 + y3 = 279 ------(i)Converting (11111)2 to decimal form, we get,x + y = (11111)2 = 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20? x + y = 16 + 8 + 4 + 2 + 1? x + y = 31 ------(ii)Also, we know that, x3 + y3 = (x + y) (x2 - xy + y2)? x3 + y3 = (x + y) (x2 - 2xy + y2 + xy)? x3 + y3 = (x + y) [(x - y)2 + xy]? (x - y)2 + xy = \(\displaystyle \frac{x^3+y^3}{x+y}\)Putting the value of equation (i) and (ii), we get,? (x - y)2 + xy = \(\displaystyle \frac{279}{31}=9\)Now, convert this decimal number 9 into binary form, 9 = (1001)2The value of (x - y)2 + xy = (1001)2