Solve {l}{25x^{4}+100x^{3}+100x^2}{x^4y^2-x^2}

$$\left. \begin{array} { l } { 25 x ^ { 4 } + 100 x ^ { 3 } + 100 x ^ { 2 } } \\ { x ^ { 4 } y ^ { 2 } - x ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$25\left(x\left(x+2\right)\right)^{2}\left(\left(xy\right)^{2}-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-x^{2}+y^{2}x^{4}=x^{2}\left(xy-1\right)\left(xy+1\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$25x^{2}\left(x+2\right)^{2}\left(xy-1\right)\left(xy+1\right)$$

Expand the expression.

$$-25x^{4}-100x^{3}-100x^{2}+25y^{2}x^{6}+100y^{2}x^{5}+100y^{2}x^{4}$$

Evaluate

$$25\left(x\left(x+2\right)\right)^{2},\ x^{2}\left(\left(xy\right)^{2}-1\right)$$