Solve {l}{(p-k)(p+k)}{(x-y)(x+y)}{(y-k)(y+k)}

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

Least Common Multiple

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

Solution Steps

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

$$-\left(k-y\right)\left(p-k\right)\left(x-y\right)\left(k+p\right)\left(y+k\right)\left(x+y\right)$$

Expand the expression.

$$p^{2}x^{2}y^{2}-k^{2}p^{2}x^{2}-k^{2}x^{2}y^{2}+x^{2}k^{4}+k^{2}y^{4}-p^{2}y^{4}+k^{2}p^{2}y^{2}-y^{2}k^{4}$$

Evaluate

$$p^{2}-k^{2},\ x^{2}-y^{2},\ y^{2}-k^{2}$$