Question

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

Answer 1

`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)`