Solve 8x^2-24x-4x^2y+12xy

$$8 x ^ { 2 } - 24 x - 4 x ^ { 2 } y + 12 x y$$

Factor

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

Solution Steps

Factor out 4.

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

Consider 2x^{2}-6x-x^{2}y+3xy. Factor out x.

$$x\left(2x-6-xy+3y\right)$$

Consider 2x-6-xy+3y. Do the grouping 2x-6-xy+3y=\left(2x-6\right)+\left(-xy+3y\right), and factor out 2 in the first and -y in the second group.

$$2\left(x-3\right)-y\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(2-y\right)$$

Rewrite the complete factored expression.

$$4x\left(-y+2\right)\left(x-3\right)$$

Evaluate

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