Solve -64x^3+144x^2y-108xy^2+27y^3

$$- 64 x ^ { 3 } + 144 x ^ { 2 } y - 108 x y ^ { 2 } + 27 y ^ { 3 }$$

Factor

$$-\left(4x-3y\right)^{3}$$

Solution Steps

Consider -64x^{3}+144x^{2}y-108xy^{2}+27y^{3} as a polynomial over variable x.

$$-64x^{3}+144yx^{2}-108y^{2}x+27y^{3}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -64x^{3} and n divides the constant factor 27y^{3}. One such factor is 4x-3y. Factor the polynomial by dividing it by this factor.

$$\left(4x-3y\right)\left(-16x^{2}+24xy-9y^{2}\right)$$

Consider -16x^{2}+24xy-9y^{2}. Consider -16x^{2}+24xy-9y^{2} as a polynomial over variable x.

$$-16x^{2}+24yx-9y^{2}$$

Find one factor of the form px^{q}+u, where px^{q} divides the monomial with the highest power -16x^{2} and u divides the constant factor -9y^{2}. One such factor is 4x-3y. Factor the polynomial by dividing it by this factor.

$$\left(4x-3y\right)\left(-4x+3y\right)$$

Rewrite the complete factored expression.

$$\left(-4x+3y\right)\left(4x-3y\right)^{2}$$

Evaluate

$$-\left(4x-3y\right)^{3}$$