Solve {l}{(m^{2}+n^{2})+(-3mn+4n^{2}-5m^{2}-5n^{2})-4m^{2}-3}{(x^{4}-y^{4})+(-5x^{2}y^2-8+2x^4)+(-4x^4+7x^3y+10x)}

$$\left. \begin{array} { l } { ( m ^ { 2 } + n ^ { 2 } ) + ( - 3 m n + 4 n ^ { 2 } - 5 m ^ { 2 } - 5 n ^ { 2 } ) - 4 m ^ { 2 } - 3 } \\ { ( x ^ { 4 } - y ^ { 4 } ) + ( - 5 x ^ { 2 } y ^ { 2 } - 8 + 2 x ^ { 4 } ) + ( - 4 x ^ { 4 } + 7 x ^ { 3 } y + 10 x ) } \end{array} \right.$$

Least Common Multiple

$$\left(3mn+8m^{2}+3\right)\left(x^{4}-10x+y^{4}-7yx^{3}+5\left(xy\right)^{2}+8\right)$$

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.

$$\left(3mn+8m^{2}+3\right)\left(x^{4}+5x^{2}y^{2}-10x+y^{4}-7yx^{3}+8\right)$$

Expand the expression.

$$3mnx^{4}+8m^{2}x^{4}+3x^{4}+15mnx^{2}y^{2}+40m^{2}x^{2}y^{2}+15x^{2}y^{2}-30mnx-80xm^{2}-30x+3mny^{4}+8m^{2}y^{4}+3y^{4}-21mnyx^{3}-56ym^{2}x^{3}-21yx^{3}+24mn+64m^{2}+24$$

Evaluate

$$-3mn-8m^{2}-3,\ -x^{4}+10x-y^{4}+7yx^{3}-5\left(xy\right)^{2}-8$$