Solve {l}{x^2+25}{75x^2-48y^2}

$$\left. \begin{array} { l } { x ^ { 2 } + 25 } \\ { 75 x ^ { 2 } - 48 y ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$-3\left(x^{2}+25\right)\left(25x^{2}-16y^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$75x^{2}-48y^{2}=3\left(5x-4y\right)\left(5x+4y\right)$$

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

$$-3\left(5x-4y\right)\left(5x+4y\right)\left(x^{2}+25\right)$$

Expand the expression.

$$-75x^{4}+48x^{2}y^{2}-1875x^{2}+1200y^{2}$$

Evaluate

$$x^{2}+25,\ 75x^{2}-48y^{2}$$