The polynomial P(x,y)=x3−8y3−6x2y+12xy2 can be expressed as the product of two polynomials.
a. (i) Group suitable terms and factorise P(x,y) completely.
b. (ii) Hence, write P(x,y) as a product involving a binomial and a trinomial.
c. (iii) Show that substituting x=2y in your factorised form gives P(2y,y)=0 and interpret this result in terms of the factors obtained.