Solve a^{2}-2ab-3b^{2}+a^{3}b-6a^2b^2+9ab^3,ab^2+b

$$a ^ { 2 } - 2 a b - 3 b ^ { 2 } + a ^ { 3 } b - 6 a ^ { 2 } b ^ { 2 } + 9 a b ^ { 3 } , a b ^ { 2 } + b$$

Least Common Multiple

$$b\left(a-3b\right)\left(ab+1\right)\left(b+ba^{2}+a-3ab^{2}\right)$$

Solution Steps

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$b\left(a-3b\right)\left(ab+1\right)\left(b+ba^{2}+a-3ab^{2}\right)$$

Expand the expression.

$$-6a^{3}b^{4}+9a^{2}b^{5}-8a^{2}b^{3}+6ab^{4}-2ab^{2}+b^{3}a^{4}-3b^{3}+2b^{2}a^{3}+ba^{2}$$

Evaluate

$$\left(a-3b\right)\left(b+ba^{2}+a-3ab^{2}\right),b\left(ab+1\right)$$