Solve {l}{25x^{2}-81y^2}{100x^4z^2-16y^2}

$$\left. \begin{array} { l } { 25 x ^ { 2 } - 81 y ^ { 2 } } \\ { 100 x ^ { 4 } z ^ { 2 } - 16 y ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$4\left(25x^{2}-81y^{2}\right)\left(4y^{2}-25\left(zx^{2}\right)^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$25x^{2}-81y^{2}=\left(5x-9y\right)\left(5x+9y\right) 100x^{4}z^{2}-16y^{2}=4\left(-2y+5zx^{2}\right)\left(2y+5zx^{2}\right)$$

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

$$4\left(-5x-9y\right)\left(5x-9y\right)\left(-2y-5zx^{2}\right)\left(2y-5zx^{2}\right)$$

Expand the expression.

$$400x^{2}y^{2}-1296y^{4}+8100y^{2}z^{2}x^{4}-2500z^{2}x^{6}$$

Evaluate

$$25x^{2}-81y^{2},\ 100z^{2}x^{4}-16y^{2}$$