Solve 6x^2y-24x^2-18y+72

$$6 { x }^{ 2 } y-24 { x }^{ 2 } -18y+72$$

Factor

$$6\left(y-4\right)\left(x^{2}-3\right)$$

Solution Steps

Factor out 6.

$$6\left(x^{2}y-4x^{2}-3y+12\right)$$

Consider x^{2}y-4x^{2}-3y+12. Do the grouping x^{2}y-4x^{2}-3y+12=\left(x^{2}y-4x^{2}\right)+\left(-3y+12\right), and factor out x^{2} in the first and -3 in the second group.

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

Factor out common term y-4 by using distributive property.

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

Rewrite the complete factored expression. Polynomial x^{2}-3 is not factored since it does not have any rational roots.

$$6\left(y-4\right)\left(x^{2}-3\right)$$

Evaluate

$$6\left(y-4\right)\left(x^{2}-3\right)$$