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

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

Least Common Multiple

$$8a^{2}+36a+100$$

Solution Steps

Factor the expressions that are not already factored.

$$4=2^{2}$$

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

$$4\left(2a^{2}+9a+25\right)$$

Expand the expression.

$$8a^{2}+36a+100$$

Evaluate

$$2a^{2}+9a+25,\ 4$$