$$9 { x }^{ 3 } -21 { x }^{ 2 } y+16x { y }^{ 2 } -4 { y }^{ 3 }$$
Factor
$\left(x-y\right)\left(3x-2y\right)^{2}$
Solution Steps
Consider $9x^{3}-21x^{2}y+16xy^{2}-4y^{3}$ as a polynomial over variable $x$.
$$9x^{3}-21yx^{2}+16y^{2}x-4y^{3}$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $9x^{3}$ and $n$ divides the constant factor $-4y^{3}$. One such factor is $3x-2y$. Factor the polynomial by dividing it by this factor.
Consider $3x^{2}-5xy+2y^{2}$. Consider $3x^{2}-5xy+2y^{2}$ as a polynomial over variable $x$.
$$3x^{2}-5yx+2y^{2}$$
Find one factor of the form $px^{q}+u$, where $px^{q}$ divides the monomial with the highest power $3x^{2}$ and $u$ divides the constant factor $2y^{2}$. One such factor is $3x-2y$. Factor the polynomial by dividing it by this factor.
