Solve 30a^4x-15a^3xz-10a^3y+5a^2yz

$$30 a ^ { 4 } x - 15 a ^ { 3 } x z - 10 a ^ { 3 } y + 5 a ^ { 2 } y z$$

Factor

$$5\left(2a-z\right)a^{2}\left(3ax-y\right)$$

Solution Steps

Factor out 5.

$$5\left(6a^{4}x-3a^{3}xz-2a^{3}y+a^{2}yz\right)$$

Consider 6a^{4}x-3a^{3}xz-2a^{3}y+a^{2}yz. Factor out a^{2}.

$$a^{2}\left(6a^{2}x-3axz-2ay+yz\right)$$

Consider 6a^{2}x-3axz-2ay+yz. Do the grouping 6a^{2}x-3axz-2ay+yz=\left(6a^{2}x-3axz\right)+\left(-2ay+yz\right), and factor out 3ax in the first and -y in the second group.

$$3ax\left(-z+2a\right)-y\left(-z+2a\right)$$

Factor out common term -z+2a by using distributive property.

$$\left(-z+2a\right)\left(3ax-y\right)$$

Rewrite the complete factored expression.

$$5a^{2}\left(-z+2a\right)\left(3ax-y\right)$$

Evaluate

$$5\left(2a-z\right)a^{2}\left(3ax-y\right)$$