Solve ay^2-3aby+2ab^2

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

Factor

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

Solution Steps

Factor out a.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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