Solve 5x^3y-10x^3+20x^2y-40x^2

$$5 x ^ { 3 } y - 10 x ^ { 3 } + 20 x ^ { 2 } y - 40 x ^ { 2 }$$

Factor

$$5\left(y-2\right)\left(x+4\right)x^{2}$$

Solution Steps

Factor out 5.

$$5\left(x^{3}y-2x^{3}+4x^{2}y-8x^{2}\right)$$

Consider x^{3}y-2x^{3}+4x^{2}y-8x^{2}. Factor out x^{2}.

$$x^{2}\left(xy-2x+4y-8\right)$$

Consider xy-2x+4y-8. Do the grouping xy-2x+4y-8=\left(xy-2x\right)+\left(4y-8\right), and factor out x in the first and 4 in the second group.

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

Factor out common term y-2 by using distributive property.

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

Rewrite the complete factored expression.

$$5x^{2}\left(y-2\right)\left(x+4\right)$$

Evaluate

$$5\left(y-2\right)\left(x+4\right)x^{2}$$