Solve {l}{(6xy-2x^2+4y)+(-2x^2-3y+5xy)}{(7km^2+4km+k)-(5k-2km+8km^2)}

$$\left. \begin{array} { l } { ( 6 x y - 2 x ^ { 2 } + 4 y ) + ( - 2 x ^ { 2 } - 3 y + 5 x y ) } \\ { ( 7 k m ^ { 2 } + 4 k m + k ) - ( 5 k - 2 k m + 8 k m ^ { 2 } ) } \end{array} \right.$$

Least Common Multiple

$$k\left(24mx^{2}-16x^{2}+11xym^{2}-66mxy+44xy+ym^{2}-6my+4y-4\left(mx\right)^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-4k+6km-km^{2}=-k\left(m-\left(\sqrt{5}+3\right)\right)\left(m-\left(-\sqrt{5}+3\right)\right)$$

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

$$k\left(4y-6my+ym^{2}+44xy-66mxy+11xym^{2}-16x^{2}+24mx^{2}-4m^{2}x^{2}\right)$$

Expand the expression.

$$-4km^{2}x^{2}+24kmx^{2}-16kx^{2}+11kxym^{2}-66kmxy+44kxy+kym^{2}-6kmy+4ky$$

Evaluate

$$y+11xy-4x^{2},\ k\left(-m^{2}+6m-4\right)$$