How do you expand ${(x - y)}^{3}$ $(x-y)^3$ ?

Question

252035 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-10T16:36:39

= $x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$ $x^3-3x^2y+3xy^2-y^3$

$(x - y) (x - y) . = x^{2} - x y - x y + y^{2}$ $(x-y)(x-y). = x^2-xy-xy+y^2$

= $x^{2} - 2 x y + y^{2}$ $x^2-2xy+y^2$

= $(x^{2} - 2 x y + y^{2}) (x - y)$ $(x^2-2xy+y^2)(x-y)$

= $x^{3} - x^{2} y - 2 x^{2} y + 2 x y^{2} + x y^{2} - y^{3}$ $x^3-x^2y-2x^2y+2xy^2+xy^2-y^3$

= $x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$ $x^3-3x^2y+3xy^2-y^3$

Answer 2 · 2018-05-08T15:47:29

$x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2}$ $x^3-y^3-3x^2y+3xy^2$

${(x - y)}^{3} = (x - y) (x - y) (x - y)$ $(x-y)^3=(x-y)(x-y)(x-y)$

Expand the first two brackets:

$(x - y) (x - y) = x^{2} - x y - x y + y^{2}$ $(x-y)(x-y)=x^2-xy-xy+y^2$

$\Rightarrow x^{2} + y^{2} - 2 x y$ $rArr x^2+y^2-2xy$

Multiply the result by the last two brackets:

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

$\Rightarrow x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2}$ $rArr x^3-y^3-3x^2y+3xy^2$

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.

How do you expand (x−y)3(x-y)^3?