Question

Rút gọn H = (a+b)^3 + (b+c)^3 +(c+a)^3 - 3(a+b)(b+c)(c+a)

Answer 1

Đặt a+b = x ; b+c = y ; c+a = z

=> H = x^3 +y^3 +z^3 -3.x.y.z

         = [x+y]^3 -3.x^2.y -3.x.y^2+ z^3 - 3.x.y.z

          = {[x+y]^3+z^3} -3.x.y[x+y+z]

          = [x+y+z].{[x+y]^2-[x+y].z+z^2} +3.x.y[x+y+z]

          = [x+y+z] . [x^2+y^2+2.x.y-x.z-y.z+z^2+3.x.y]

           = [x+y+z]. [x^2+y^2+z^2-xy-y.z-x.z]

           = [a+b+b+c+c+a]. {[a+b]^2+[b+c]^2+[c+a]^2-[a+b].[b+c]-[a+b].[a+c] - [b+c].[c+a]}

            = 2.[a+b+c] .[a^2+b^2 +b^2 +c^2 +c^2 +a^2 +2.ab.+2.bc+2.ac-ab-b^2-ac-bc-a^2-ab-ac-bc-bc-c^2-ab-ac]

            = 2.[a+b+c].[a^2+b^2+c^2-ab-ac-bc]

Answer 2

rút gọn a

(-a-b+c)-(-a-b-c)