How do you expand #(x-y)^3#?

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Answer 1 · 2018-04-10T16:36:39

=# 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#

Answer 2 · 2018-05-08T15:47:29

#x^3-y^3-3x^2y+3xy^2#

#(x-y)^3=(x-y)(x-y)(x-y)#

Expand the first two brackets:

#(x-y)(x-y)=x^2-xy-xy+y^2#

#rArr x^2+y^2-2xy#

Multiply the result by the last two brackets:

#(x^2+y^2-2xy)(x-y)=x^3-x^2y+xy^2-y^3-2x^2y+2xy^2#

#rArr x^3-y^3-3x^2y+3xy^2#

Always expand each term in the bracket by all the other terms in the other brackets, but never multiply two or more terms in the same bracket.