Solve {l}{(3-a)(-a-3)-(a+3)^{2}+3(2a-6)+(a-1)^3-3a(1-a)}{(x-1)^3+(x-1)^2-x+x(4-x)(4+x)+(8-x-4)^2}

$$\left. \begin{array} { l } { ( 3 - a ) ( - a - 3 ) - ( a + 3 ) ^ { 2 } + 3 ( 2 a - 6 ) + ( a - 1 ) ^ { 3 } - 3 a ( 1 - a ) } \\ { ( x - 1 ) ^ { 3 } + ( x - 1 ) ^ { 2 } - x + x ( 4 - x ) ( 4 + x ) + ( 8 - x - 4 ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(x^{2}-8x-16\right)\left(a^{3}-37\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$16+8x-x^{2}=-\left(x-\left(-4\sqrt{2}+4\right)\right)\left(x-\left(4\sqrt{2}+4\right)\right)$$

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

$$\left(x^{2}-8x-16\right)\left(a^{3}-37\right)$$

Expand the expression.

$$x^{2}a^{3}-37x^{2}-8xa^{3}+296x-16a^{3}+592$$

Evaluate

$$a^{3}-37,\ 16+8x-x^{2}$$