Solve -2x^2y+8xy^2-8y^3

$$- 2 x ^ { 2 } y + 8 x y ^ { 2 } - 8 y ^ { 3 }$$

Factor

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

Solution Steps

Factor out 2.

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

Consider -x^{2}y+4xy^{2}-4y^{3}. Factor out y.

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

Consider -x^{2}+4xy-4y^{2}. Consider -x^{2}+4xy-4y^{2} as a polynomial over variable x.

$$-x^{2}+4yx-4y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -x^{2} and n divides the constant factor -4y^{2}. One such factor is x-2y. Factor the polynomial by dividing it by this factor.

$$\left(x-2y\right)\left(-x+2y\right)$$

Rewrite the complete factored expression.

$$2y\left(x-2y\right)\left(-x+2y\right)$$

Evaluate

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