How do you expand the binomial #(4x-4y)^3#?

1 Answer
Oct 23, 2016

#64x^3-192x^2y+192xy^2-64y^3#

Explanation:

The cubic difference of a binomial is:
#color(red)((a-b)^3=a^3-3a^2b+3ab^2-b^#

#(4x-4y)^3=color(red)((4x)^3-3(4x)^2(4y)+3(4x)(4y)^2_(4y)^3)#
#(4x-4y)^3=64x^3-3(16x^2)(4y)+3(4x)(16y^2)-64y^3#
#(4x-4y)^3=64x^3-192x^2y+192xy^2-64y^3#

There is not like polynomials in the above expanded form
hint: #color(blue)(x^2y!=xy^2)#