Solve 3a^2-15a^3y+18a^4y^2=

$$3 a ^ { 2 } - 15 a ^ { 3 } y + 18 a ^ { 4 } y ^ { 2 } =$$

Factor

$$3a^{2}\left(2ay-1\right)\left(3ay-1\right)$$

Solution Steps

Factor out 3.

$$3\left(a^{2}-5a^{3}y+6a^{4}y^{2}\right)$$

Consider a^{2}-5a^{3}y+6a^{4}y^{2}. Factor out a^{2}.

$$a^{2}\left(1-5ay+6a^{2}y^{2}\right)$$

Consider 1-5ay+6a^{2}y^{2}. Consider 1-5ay+6a^{2}y^{2} as a polynomial over variable a.

$$6y^{2}a^{2}-5ya+1$$

Find one factor of the form ky^{m}a^{n}+p, where ky^{m}a^{n} divides the monomial with the highest power 6y^{2}a^{2} and p divides the constant factor 1. One such factor is 2ay-1. Factor the polynomial by dividing it by this factor.

$$\left(2ay-1\right)\left(3ay-1\right)$$

Rewrite the complete factored expression.

$$3a^{2}\left(2ay-1\right)\left(3ay-1\right)$$

Evaluate

$$3a^{2}\left(2ay-1\right)\left(3ay-1\right)$$