Solve {l}{x^2-y^2-4x+4}{9x^2-y^2-4y-4}

$$\left. \begin{array} { l } { x ^ { 2 } - y ^ { 2 } - 4 x + 4 } \\ { 9 x ^ { 2 } - y ^ { 2 } - 4 y - 4 } \end{array} \right.$$

Least Common Multiple

$$\left(-\left(-y-2\right)^{2}+9x^{2}\right)\left(\left(x-2\right)^{2}-y^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-y^{2}+\left(x-2\right)^{2}=\left(-x+y+2\right)\left(-x-y+2\right) 9x^{2}-\left(y+2\right)^{2}=\left(3x-y-2\right)\left(3x+y+2\right)$$

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

$$\left(x-y-2\right)\left(3x-y-2\right)\left(x+y-2\right)\left(3x+y+2\right)$$

Expand the expression.

$$9x^{4}-36x^{3}-10x^{2}y^{2}+32x^{2}+4xy^{2}+16xy+16x+y^{4}+4y^{3}-4yx^{2}-16y-16$$

Evaluate

$$\left(x-2\right)^{2}-y^{2},\ -\left(y+2\right)^{2}+9x^{2}$$