How do you factor 8 minus 27x cubed?

Answer 1

Remember 8 = 2^(3) & 27x^(3) = (3x)^3

Hence

2^(3) - (3x)^3 is of the form

x^(3) - y^(3) = ( x - y)(x^2 + xy + y^2)

Hence

2^(3) - (3x)^(3) = ( 2 - 3y)(2^(2) + (2)(3y) + (3y)^(2)) =>

2^(3) - (3y)^(3) = (2 - 3y)(4 + 6y + 9y^(2)) -

Done!!!!!

Answer 2

(2 - 3x)(9x^2 + 6x + 4)