Solve {l}{(x-y)(x+y)}{(p+q)(p-q)}{(p-5)(p+5)}

$$\left. \begin{array} { l } { ( x - y ) ( x + y ) } \\ { ( p + q ) ( p - q ) } \\ { ( p - 5 ) ( p + 5 ) } \end{array} \right.$$

Least Common Multiple

$$\left(p^{2}-25\right)\left(p^{2}-q^{2}\right)\left(x^{2}-y^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}-y^{2}=\left(x+y\right)\left(x-y\right) p^{2}-q^{2}=\left(p+q\right)\left(p-q\right) -25+p^{2}=\left(p-5\right)\left(p+5\right)$$

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

$$\left(p-5\right)\left(p+5\right)\left(p-q\right)\left(x-y\right)\left(p+q\right)\left(x+y\right)$$

Expand the expression.

$$x^{2}p^{4}-p^{2}q^{2}x^{2}+25q^{2}x^{2}-25p^{2}x^{2}+p^{2}q^{2}y^{2}-y^{2}p^{4}+25p^{2}y^{2}-25q^{2}y^{2}$$

Evaluate

$$x^{2}-y^{2},\ p^{2}-q^{2},\ p^{2}-25$$