Solve {l}{(x-3)(x+2)-(2x+1)(x-4)+2(x-3)(x+4)}{(2a+1)(a^2-a+1)-2(a^2-4)(a+3)+(-3a)^2}

$$\left. \begin{array} { l } { ( x - 3 ) ( x + 2 ) - ( 2 x + 1 ) ( x - 4 ) + 2 ( x - 3 ) ( x + 4 ) } \\ { ( 2 a + 1 ) ( a ^ { 2 } - a + 1 ) - 2 ( a ^ { 2 } - 4 ) ( a + 3 ) + ( - 3 a ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$9ax^{2}+25x^{2}+16xa^{2}+72ax+200x+2\left(ax\right)^{2}-52a^{2}-234a-650$$

Solution Steps

Factor the expressions that are not already factored.

$$-26+8x+x^{2}=\left(x-\left(\sqrt{42}-4\right)\right)\left(x-\left(-\sqrt{42}-4\right)\right)$$

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

$$2a^{2}x^{2}+9ax^{2}+25x^{2}+16xa^{2}+72ax+200x-52a^{2}-234a-650$$

Evaluate

$$x^{2}+8x-26,\ 2a^{2}+9a+25$$