Solve {l}{(x-2)(x-11)-2x(4-3x)}{(a+6)(a-2)+(a-4)(a+1)}

$$\left. \begin{array} { l } { ( x - 2 ) ( x - 11 ) - 2 x ( 4 - 3 x ) } \\ { ( a + 6 ) ( a - 2 ) + ( a - 4 ) ( a + 1 ) } \end{array} \right.$$

Least Common Multiple

$$7ax^{2}-112x^{2}-42xa^{2}-21ax+336x+14\left(ax\right)^{2}+44a^{2}+22a-352$$

Solution Steps

Factor the expressions that are not already factored.

$$2a^{2}+a-16=2\left(a-\left(-\frac{1}{4}\sqrt{129}-\frac{1}{4}\right)\right)\left(a-\left(\frac{1}{4}\sqrt{129}-\frac{1}{4}\right)\right)$$

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

$$14a^{2}x^{2}+7ax^{2}-112x^{2}-42xa^{2}-21ax+336x+44a^{2}+22a-352$$

Evaluate

$$7x^{2}-21x+22,\ 2a^{2}+a-16$$