Wie erweitert man # (xy) ^ 3 #?
Antworten:
=# x^3-3x^2y+3xy^2-y^3#
Erläuterung:
#(x-y)(x-y). = x^2-xy-xy+y^2#
=#x^2-2xy+y^2#
=#(x^2-2xy+y^2)(x-y)#
=# x^3-x^2y-2x^2y+2xy^2+xy^2-y^3#
=# x^3-3x^2y+3xy^2-y^3#
=# x^3-3x^2y+3xy^2-y^3#
#(x-y)(x-y). = x^2-xy-xy+y^2#
=#x^2-2xy+y^2#
=#(x^2-2xy+y^2)(x-y)#
=# x^3-x^2y-2x^2y+2xy^2+xy^2-y^3#
=# x^3-3x^2y+3xy^2-y^3#