Solve {l}{(2x-y)^2-(2x-y)}{(2x+y)+(2y)^4}{1/1(3y)^2}

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

Least Common Multiple

$$9\left(2x-y\right)\left(2x-y-1\right)y^{2}\left(2x+16y^{4}+y\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-2x+y+\left(2x-y\right)^{2}=\left(2x-y\right)\left(2x-y-1\right)$$

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

$$9\left(2x-y\right)\left(2x-y-1\right)y^{2}\left(2x+16y^{4}+y\right)$$

Expand the expression.

$$576x^{2}y^{6}-36x^{2}y^{3}-36x^{2}y^{2}-576xy^{7}-288xy^{6}-18xy^{4}+144y^{8}+144y^{7}+9y^{5}+9y^{4}+72y^{2}x^{3}$$

Evaluate

$$\left(2x-y\right)^{2}+y-2x,\ 2x+16y^{4}+y,\ 9y^{2}$$