Solve 40w^{5}z^{2}-200w^5z^3+250w^5z^4

$$40 w ^ { 5 } z ^ { 2 } - 200 w ^ { 5 } z ^ { 3 } + 250 w ^ { 5 } z ^ { 4 }$$

Factor

$$10z^{2}\left(5z-2\right)^{2}w^{5}$$

Solution Steps

Factor out 10.

$$10\left(4w^{5}z^{2}-20w^{5}z^{3}+25w^{5}z^{4}\right)$$

Consider 4w^{5}z^{2}-20w^{5}z^{3}+25w^{5}z^{4}. Factor out w^{5}z^{2}.

$$w^{5}z^{2}\left(4-20z+25z^{2}\right)$$

Consider 4-20z+25z^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=5z and b=2.

$$\left(5z-2\right)^{2}$$

Rewrite the complete factored expression.

$$10w^{5}z^{2}\left(5z-2\right)^{2}$$

Evaluate

$$10w^{5}\left(z\left(5z-2\right)\right)^{2}$$