Solve {l}{a^{2}+2ab+b^2-2a^2+3ab*a^2b(a-b)}{(abb-a^2)(a-2b)(a+2b)}

$$\left. \begin{array} { l } { a ^ { 2 } + 2 a b + b ^ { 2 } - 2 a ^ { 2 } + 3 a b \cdot a ^ { 2 } b ( a - b ) } \\ { ( a b b - a ^ { 2 } ) ( a - 2 b ) ( a + 2 b ) } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$a^{6}-12a^{5}b^{6}-12a^{5}b^{5}+12a^{4}b^{7}+5a^{3}b^{4}+8a^{3}b^{3}-8a^{2}b^{5}+4a^{2}b^{4}-4ab^{6}-3b^{5}a^{6}+3b^{4}a^{7}+12b^{4}a^{6}+3b^{3}a^{7}+2b^{3}a^{4}-3b^{2}a^{8}-b^{2}a^{5}-5b^{2}a^{4}-2ba^{5}$$

Evaluate

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