Question

Prove that (x+y) ^3-(x-y)^3=6y(x^2-y^2)-4y^3​

Answer 1

Answer:

$(x + y) {}^{3} - (x - y) {}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} - {x}^{3} + 3 {x}^{2} y - 3x {y}^{2} + {y}^{3} = 6 {x}^{2} y + 2 {y}^{3} = 6 {x}^{2} y + 6 {y}^{3} - 4 {y}^{3} = 6y( {x}^{2} + {y}^{2} ) - 4 {y}^{3}$