Solve {l}{[(x^{2}+2)^{2}-4x^{2}]^{2}-2(2x^{2}-1)(2x^{2}+1)-(x^{5})^{2}:x^{2}}{(x^{2}+x+1)(x^{2}-x-1)-(x^{2}+x-1)(x^{2}+x+1)+2x(x^{2}+1)}{(a-b+c)(a-b-c)-(a+b+c)(a-b-c)+2b(a-b)}{(a^{3}+a^{2}-2a+1)(a^{3}+a^{2}+2a-1)+a^2(4-a^2-2a^3)-a(a^5+4)}

$$\left. \begin{array} { l } { [ ( x ^ { 2 } + 2 ) ^ { 2 } - 4 x ^ { 2 } ] ^ { 2 } - 2 ( 2 x ^ { 2 } - 1 ) ( 2 x ^ { 2 } + 1 ) - ( x ^ { 5 } ) ^ { 2 } : x ^ { 2 } } \\ { ( x ^ { 2 } + x + 1 ) ( x ^ { 2 } - x - 1 ) - ( x ^ { 2 } + x - 1 ) ( x ^ { 2 } + x + 1 ) + 2 x ( x ^ { 2 } + 1 ) } \\ { ( a - b + c ) ( a - b - c ) - ( a + b + c ) ( a - b - c ) + 2 b ( a - b ) } \\ { ( a ^ { 3 } + a ^ { 2 } - 2 a + 1 ) ( a ^ { 3 } + a ^ { 2 } + 2 a - 1 ) + a ^ { 2 } ( 4 - a ^ { 2 } - 2 a ^ { 3 } ) - a ( a ^ { 5 } + 4 ) } \end{array} \right.$$

Least Common Multiple

$$18bcx^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$18=2\times 3^{2}$$

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

$$18bcx^{2}$$

Evaluate

$$18,\ -2x^{2},\ 2bc,\ -1$$