Solve 2a^2y-3ay^2-3ay^2+y^3+3{y}^3

$$2 { a }^{ 2 } y-3a { y }^{ 2 } -3a { y }^{ 2 } + { y }^{ 3 } +3 { y }^{ 3 }$$

Factor

$$2y\left(a-y\right)\left(a-2y\right)$$

Solution Steps

Factor out y.

$$y\left(2a^{2}-3ay-3ay+y^{2}+3y^{2}\right)$$

Consider 2a^{2}-3ay-3ay+y^{2}+3y^{2}. Multiply and combine like terms.

$$4y^{2}-6ay+2a^{2}$$

Consider 4y^{2}-6ay+2a^{2}. Factor out 2.

$$2\left(2y^{2}-3ay+a^{2}\right)$$

Consider 2y^{2}-3ay+a^{2}. Consider 2y^{2}-3ay+a^{2} as a polynomial over variable y. Find one factor of the form ky^{m}+n, where ky^{m} divides the monomial with the highest power 2y^{2} and n divides the constant factor a^{2}. One such factor is 2y-a. Factor the polynomial by dividing it by this factor.

$$\left(2y-a\right)\left(y-a\right)$$

Rewrite the complete factored expression.

$$2y\left(2y-a\right)\left(y-a\right)$$

Evaluate

$$2y\left(a-y\right)\left(a-2y\right)$$