How do you simplify $(x - y)^3$ ?

Question

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Answer 1 · 2017-07-14T12:09:11

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

$(x - y)^3$

Solution

Well you can use many methods to simplify like:

Using Pascal Triangle which give be $1, 3, 3, 1$ as the expansion..

You can simplify $(x - y)^3$ to either $(x - y) (x - y) (x - y) or (x - y)^2 (x - y)$

But using those two will result in same answer which will be in this format $->$ $1, 3, 3, 1$

Hence $rArr$ $(x - y)^3 = (x - y) (x - y) (x - y)$

$(x - y) (x - y) (x - y)$

$(x - y) [(x - y) (x - y)]$

$(x - y) [x^2 - xy - xy + y^2]$

This lead to the point using difference of two cubes as:

$(x - y) [x^2 - 2xy + y^2]$

$x [x^2 - 2xy + y^2] - y [x^2 - 2xy + y^2]$

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

Collect like terms

$color(red)(x^3 - y^3) color(blue)(- 2x^2y - x^2y) color(green)(+ xy^2 + 2xy^2)$

$:.$ $x^3 - y^3 - 3x^2y + 3xy^2$ $-> Answer$

If it is the cube of a binomial, it will be in this format $rArr$ $color(red)(1)x^3 - color(red)(3)x^2y + color(red)(3)xy^2 - color(red)(1)y^3$

How do you simplify (x - y)^3 (x - y)^3?