Solve {l}{9(x-y)^{2}+14(x^{2}-y^{2})+4(x+y)^{2}}{9(x^{2}+y^{2}-2xy)+12(x^2+y^2)+4(x^2+y^2+2xy)}

$$\left. \begin{array} { l } { 9 ( x - y ) ^ { 2 } + 14 ( x ^ { 2 } - y ^ { 2 } ) + 4 ( x + y ) ^ { 2 } } \\ { 9 ( x ^ { 2 } + y ^ { 2 } - 2 x y ) + 12 ( x ^ { 2 } + y ^ { 2 } ) + 4 ( x ^ { 2 } + y ^ { 2 } + 2 x y ) } \end{array} \right.$$

Least Common Multiple

$$-675x^{4}+240xy^{3}+25y^{4}+520yx^{3}-750\left(xy\right)^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$25x^{2}-10xy+25y^{2}=5\left(5x^{2}-2xy+5y^{2}\right)$$

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

$$5\left(104yx^{3}+5y^{4}+48xy^{3}-150x^{2}y^{2}-135x^{4}\right)$$

Expand the expression.

$$-675x^{4}-750x^{2}y^{2}+240xy^{3}+25y^{4}+520yx^{3}$$

Evaluate

$$27x^{2}-10xy-y^{2},\ 25x^{2}-10xy+25y^{2}$$