Solve {l}{ab^{2}+ac^{2}+bc^2+ba^2}{ca^2+cb^2}

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

Least Common Multiple

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

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.

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

Expand the expression.

$$a^{3}c^{3}+ab^{2}c^{3}+acb^{4}+b^{3}c^{3}+ba^{2}c^{3}+bca^{4}+ca^{2}b^{3}+cb^{2}a^{3}$$

Evaluate

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