Solve 3a^{2}b^{2}c^{2}-12a^{2}b^2c^2+9ab^2c^3

$$3 a ^ { 2 } b ^ { 2 } c ^ { 2 } - 12 a ^ { 2 } b ^ { 2 } c ^ { 2 } + 9 a b ^ { 2 } c ^ { 3 }$$

Factor

$$9a\left(c-a\right)b^{2}c^{2}$$

Solution Steps

Factor out 3.

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

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

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

Consider a-4a+3c. Multiply and combine like terms.

$$-3a+3c$$

Consider -3a+3c. Factor out 3.

$$3\left(-a+c\right)$$

Rewrite the complete factored expression.

$$9ab^{2}c^{2}\left(-a+c\right)$$

Simplify.

$$9a\left(-a+c\right)b^{2}c^{2}$$

Evaluate

$$9a\left(c-a\right)\left(bc\right)^{2}$$