Solve 144x^{3}y^4+28x^2y^5-60xy^6

$$144 x ^ { 3 } y ^ { 4 } + 28 x ^ { 2 } y ^ { 5 } - 60 x y ^ { 6 }$$

Factor

$$4x\left(9x-5y\right)\left(4x+3y\right)y^{4}$$

Solution Steps

Factor out 4.

$$4\left(36x^{3}y^{4}+7x^{2}y^{5}-15xy^{6}\right)$$

Consider 36x^{3}y^{4}+7x^{2}y^{5}-15xy^{6}. Factor out xy^{4}.

$$xy^{4}\left(36x^{2}+7xy-15y^{2}\right)$$

Consider 36x^{2}+7xy-15y^{2}. Consider 36x^{2}+7xy-15y^{2} as a polynomial over variable x.

$$36x^{2}+7yx-15y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 36x^{2} and n divides the constant factor -15y^{2}. One such factor is 4x+3y. Factor the polynomial by dividing it by this factor.

$$\left(4x+3y\right)\left(9x-5y\right)$$

Rewrite the complete factored expression.

$$4xy^{4}\left(4x+3y\right)\left(9x-5y\right)$$

Evaluate

$$4x\left(9x-5y\right)\left(4x+3y\right)y^{4}$$