Solve 0a^{4}b^{2}+36a^{2}b^{3}-3a^{2}b^{4}-18b^5+3a^2b^2+18b^3

$$0 a ^ { 4 } b ^ { 2 } + 36 a ^ { 2 } b ^ { 3 } - 3 a ^ { 2 } b ^ { 4 } - 18 b ^ { 5 } + 3 a ^ { 2 } b ^ { 2 } + 18 b ^ { 3 }$$

Factor

$$3b^{2}\left(6b+12ba^{2}-6b^{3}+a^{2}-a^{2}b^{2}\right)$$

Solution Steps

Factor out 3.

$$3\left(0+12a^{2}b^{3}-a^{2}b^{4}-6b^{5}+a^{2}b^{2}+6b^{3}\right)$$

Consider 12a^{2}b^{3}-a^{2}b^{4}-6b^{5}+a^{2}b^{2}+6b^{3}. Factor out b^{2}.

$$b^{2}\left(12a^{2}b-a^{2}b^{2}-6b^{3}+a^{2}+6b\right)$$

Rewrite the complete factored expression.

$$3b^{2}\left(12a^{2}b-a^{2}b^{2}-6b^{3}+a^{2}+6b\right)$$

Evaluate

$$3b^{2}\left(a^{2}-6b^{3}+12ba^{2}+6b-\left(ab\right)^{2}\right)$$