Solve 4xy-8xy^2-12xy^3=

$$4 x y - 8 x y ^ { 2 } - 12 x y ^ { 3 } =$$

Factor

$$-4xy\left(3y-1\right)\left(y+1\right)$$

Solution Steps

Factor out 4.

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

Consider xy-2xy^{2}-3xy^{3}. Factor out xy.

$$xy\left(1-2y-3y^{2}\right)$$

Consider 1-2y-3y^{2}. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$-3y^{2}-2y+1$$

Factor the expression by grouping. First, the expression needs to be rewritten as -3y^{2}+ay+by+1. To find a and b, set up a system to be solved.

$$a+b=-2 ab=-3=-3$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.

$$a=1 b=-3$$

Rewrite -3y^{2}-2y+1 as \left(-3y^{2}+y\right)+\left(-3y+1\right).

$$\left(-3y^{2}+y\right)+\left(-3y+1\right)$$

Factor out -y in the first and -1 in the second group.

$$-y\left(3y-1\right)-\left(3y-1\right)$$

Factor out common term 3y-1 by using distributive property.

$$\left(3y-1\right)\left(-y-1\right)$$

Rewrite the complete factored expression.

$$4xy\left(3y-1\right)\left(-y-1\right)$$

Evaluate

$$-4xy\left(3y-1\right)\left(y+1\right)$$