The polynomial can be expressed as the product of two polynomials.
MATHEMATICS · Multi-part · AoPS · Mathematics · Special Factorizations · Special Factorizations
Problem
The polynomial P(x,y)=x3−8y3−6x2y+12xy2 can be expressed as the product of two polynomials.
(i) Group suitable terms and factorise P(x,y) completely.
(ii) Hence, write P(x,y) as a product involving a binomial and a trinomial.
(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.