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

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

Least Common Multiple

$$2\left(4x^{2}-9\right)\left(x^{2}+9\right)\left(2x^{2}+10x+13\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2x^{2}+18=2\left(x^{2}+9\right) -18+8x^{2}=2\left(2x-3\right)\left(2x+3\right)$$

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

$$2\left(2x-3\right)\left(2x+3\right)\left(x^{2}+9\right)\left(2x^{2}+10x+13\right)$$

Expand the expression.

$$16x^{6}+80x^{5}+212x^{4}+540x^{3}+378x^{2}-1620x-2106$$

Evaluate

$$2x^{2}+18,\ 8x^{2}-18,\ \left(x+2\right)^{2}+\left(x+3\right)^{2}$$