Solve {l}{11x(2+y)-3(x+4y)}{(3xy-2x)(2x^2-3y)}{(x+3)(x-3)}

$$\left. \begin{array} { l } { 11 x ( 2 + y ) - 3 ( x + 4 y ) } \\ { ( 3 x y - 2 x ) ( 2 x ^ { 2 } - 3 y ) } \\ { ( x + 3 ) ( x - 3 ) } \end{array} \right.$$

Least Common Multiple

$$x\left(3y-2\right)\left(x^{2}-9\right)\left(2x^{2}-3y\right)\left(12y-19x-11xy\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{2}-9=\left(x-3\right)\left(x+3\right)$$

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

$$x\left(x-3\right)\left(3y-2\right)\left(x+3\right)\left(2x^{2}-3y\right)\left(12y-19x-11xy\right)$$

Expand the expression.

$$76x^{6}-684x^{4}-108x^{3}y^{3}-891x^{2}y^{3}-945x^{2}y^{2}+972xy^{3}-648xy^{2}+99y^{3}x^{4}-66y^{2}x^{6}+72y^{2}x^{5}+699y^{2}x^{4}-576y^{2}x^{3}-70yx^{6}-48yx^{5}+516yx^{4}+432yx^{3}+1026yx^{2}$$

Evaluate

$$11xy+19x-12y,\ x\left(3y-2\right)\left(2x^{2}-3y\right),\ x^{2}-9$$