Solve 4xy^4z^3-4xyz^3=

$$4 x y ^ { 4 } z ^ { 3 } - 4 x y z ^ { 3 } =$$

Factor

$$4xy\left(y-1\right)\left(y^{2}+y+1\right)z^{3}$$

Solution Steps

Factor out 4.

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

Consider xy^{4}z^{3}-xyz^{3}. Factor out xyz^{3}.

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

Consider y^{3}-1. Rewrite y^{3}-1 as y^{3}-1^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

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

Rewrite the complete factored expression. Polynomial y^{2}+y+1 is not factored since it does not have any rational roots.

$$4xyz^{3}\left(y-1\right)\left(y^{2}+y+1\right)$$

Evaluate

$$4xyz^{3}\left(y^{3}-1\right)$$