Solve {l}{x^{6}+x^{5}+x^{3}}{ab^{2}+ab^{3}+a^2b^3+ab^2+b^2c}

$$\left. \begin{array} { l } { x ^ { 6 } + x ^ { 5 } + x ^ { 3 } } \\ { a b ^ { 2 } + a b ^ { 3 } + a ^ { 2 } b ^ { 3 } + a b ^ { 2 } + b ^ { 2 } c } \end{array} \right.$$

Least Common Multiple

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

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.

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

Expand the expression.

$$a^{2}b^{3}x^{6}+ab^{3}x^{6}+cb^{2}x^{6}+2ab^{2}x^{6}+a^{2}b^{3}x^{5}+ab^{3}x^{5}+cb^{2}x^{5}+2ab^{2}x^{5}+a^{2}b^{3}x^{3}+ab^{3}x^{3}+cb^{2}x^{3}+2ab^{2}x^{3}$$

Evaluate

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