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

1 Answer
Jul 14, 2017

Answer:

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

Explanation:

# (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 #