Solve 100a^{2}b^{3}c-150ab^{2}c^2+50ab^3c^3-200abc^2

$$100 a ^ { 2 } b ^ { 3 } c - 150 a b ^ { 2 } c ^ { 2 } + 50 a b ^ { 3 } c ^ { 3 } - 200 a b c ^ { 2 }$$

Factor

$$50abc\left(2ab^{2}+b^{2}c^{2}-3bc-4c\right)$$

Solution Steps

Factor out 50.

$$50\left(2a^{2}b^{3}c-3ab^{2}c^{2}+ab^{3}c^{3}-4abc^{2}\right)$$

Consider 2a^{2}b^{3}c-3ab^{2}c^{2}+ab^{3}c^{3}-4abc^{2}. Factor out abc.

$$abc\left(2ab^{2}-3bc+b^{2}c^{2}-4c\right)$$

Rewrite the complete factored expression.

$$50abc\left(2ab^{2}-3bc+b^{2}c^{2}-4c\right)$$

Evaluate

$$50abc\left(2ab^{2}-3bc-4c+\left(bc\right)^{2}\right)$$