Solve {l}{-b^{2}b^{2}+bcquadc^{2}+bc}{a^{2}+ac-acquadc^2+ac}{a^2+ab^2}{b^2+ab-ab}

$$\left. \begin{array} { l } { - b ^ { 2 } b ^ { 2 } + b c \quad c ^ { 2 } + b c } \\ { a ^ { 2 } + a c - a c \quad c ^ { 2 } + a c } \\ { a ^ { 2 } + a b ^ { 2 } } \\ { b ^ { 2 } + a b - a b } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$-a^{3}b^{5}-a^{2}b^{7}-a^{2}b^{2}c^{6}+a^{2}b^{2}c^{4}+2a^{2}b^{2}c^{2}+a^{2}c^{3}b^{5}+a^{2}c^{3}b^{4}-ab^{4}c^{6}+ab^{4}c^{4}+ac^{3}b^{7}+2ac^{2}b^{4}-2acb^{7}+b^{2}a^{3}c^{3}-2ca^{2}b^{5}+ca^{2}b^{4}+cb^{2}a^{3}$$

Evaluate

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