Solve {l}{2x-3y*(2x+3)-(3-2x)*(3+2x)}{x+2y^2+(x+3)^2}

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

Least Common Multiple

$$81-8\left(xy\right)^{2}+81y+51yx^{2}+6yx^{3}+18y^{2}+18y^{3}+45x+117xy-4xy^{2}+12xy^{3}-41x^{2}-30x^{3}-4x^{4}$$

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.

$$81+81y+51yx^{2}+6yx^{3}+18y^{2}+18y^{3}+45x+117xy-4xy^{2}+12xy^{3}-41x^{2}-8x^{2}y^{2}-30x^{3}-4x^{4}$$

Expand the expression.

$$-4x^{4}-30x^{3}-8x^{2}y^{2}-41x^{2}+12xy^{3}-4xy^{2}+117xy+45x+18y^{3}+18y^{2}+6yx^{3}+51yx^{2}+81y+81$$

Evaluate

$$4x^{2}-6xy+2x-9y-9,\ \left(x+3\right)^{2}+2y^{2}+x$$