Solve {l}{x^{4}+y^4+x^2}{x^2+y^2+x}

$$\left. \begin{array} { l } { x ^ { 4 } + y ^ { 4 } + x ^ { 2 } } \\ { x ^ { 2 } + y ^ { 2 } + x } \end{array} \right.$$

Least Common Multiple

$$\left(x^{2}+x+y^{2}\right)\left(x^{4}+x^{2}+y^{4}\right)$$

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.

$$\left(x^{2}+x+y^{2}\right)\left(x^{4}+x^{2}+y^{4}\right)$$

Expand the expression.

$$x^{6}+x^{5}+x^{4}+x^{3}+x^{2}y^{4}+x^{2}y^{2}+xy^{4}+y^{6}+y^{2}x^{4}$$

Evaluate

$$x^{4}+x^{2}+y^{4},\ x^{2}+x+y^{2}$$