Solve {l}{4x^{4}y^{2}-28x^{3}y^{3}+40x^{2}y^{4}-48xy^{5}}{55m^{2}n^{3}x+110m^{2}n^3x^2-220m^2y^3}

$$\left. \begin{array} { l } { 4 x ^ { 4 } y ^ { 2 } - 28 x ^ { 3 } y ^ { 3 } + 40 x ^ { 2 } y ^ { 4 } - 48 x y ^ { 5 } } \\ { 55 m ^ { 2 } n ^ { 3 } x + 110 m ^ { 2 } n ^ { 3 } x ^ { 2 } - 220 m ^ { 2 } y ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$220x\left(x^{3}+10xy^{2}-12y^{3}-7yx^{2}\right)\left(4y^{3}-xn^{3}-2x^{2}n^{3}\right)\left(my\right)^{2}$$

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.

$$220xm^{2}y^{2}\left(x^{3}+10xy^{2}-12y^{3}-7yx^{2}\right)\left(4y^{3}-xn^{3}-2x^{2}n^{3}\right)$$

Expand the expression.

$$880m^{2}x^{4}y^{5}-4400m^{2}n^{3}x^{4}y^{4}-6160m^{2}x^{3}y^{6}+5280m^{2}n^{3}x^{3}y^{5}-2200m^{2}n^{3}x^{3}y^{4}+8800m^{2}x^{2}y^{7}+2640m^{2}x^{2}n^{3}y^{5}-10560xm^{2}y^{8}+3080m^{2}n^{3}y^{3}x^{5}+1540m^{2}n^{3}y^{3}x^{4}-440m^{2}y^{2}n^{3}x^{6}-220m^{2}y^{2}n^{3}x^{5}$$

Evaluate

$$4xy^{2}\left(x^{3}+10xy^{2}-12y^{3}-7yx^{2}\right),\ 55m^{2}\left(2x^{2}n^{3}+xn^{3}-4y^{3}\right)$$