Solve {l}{(4*6x^{2})+(3xy*3y)+(z)}{18x^3y+9xy^2-15x^2y^2}

$$\left. \begin{array} { l } { ( 4 \cdot 6 x ^ { 2 } ) + ( 3 x y \cdot 3 y ) + ( z ) } \\ { 18 x ^ { 3 } y + 9 x y ^ { 2 } - 15 x ^ { 2 } y ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$3xy\left(-6x^{2}+5xy-3y\right)\left(24x^{2}+9xy^{2}+z\right)$$

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.

$$3xy\left(-6x^{2}+5xy-3y\right)\left(24x^{2}+9xy^{2}+z\right)$$

Expand the expression.

$$135x^{3}y^{4}-81x^{2}y^{4}-9xzy^{2}-162y^{3}x^{4}+360y^{2}x^{4}-216y^{2}x^{3}-432yx^{5}-18yzx^{3}+15zx^{2}y^{2}$$

Evaluate

$$24x^{2}+9xy^{2}+z,\ 3xy\left(6x^{2}-5xy+3y\right)$$