Solve {l}{(x+1)(x-2)+(x+2)(x-1)}{(3k+n)(k-2n)-k(4k+n)}

$$\left. \begin{array} { l } { ( x + 1 ) ( x - 2 ) + ( x + 2 ) ( x - 1 ) } \\ { ( 3 k + n ) ( k - 2 n ) - k ( 4 k + n ) } \end{array} \right.$$

Least Common Multiple

$$2\left(x^{2}-2\right)\left(6kn+2n^{2}+k^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2x^{2}-4=2\left(x^{2}-2\right)$$

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

$$2\left(x^{2}-2\right)\left(6kn+2n^{2}+k^{2}\right)$$

Expand the expression.

$$12knx^{2}+2k^{2}x^{2}+4n^{2}x^{2}-24kn-8n^{2}-4k^{2}$$

Evaluate

$$2\left(x^{2}-2\right),\ -6kn-2n^{2}-k^{2}$$