Solve {l}{(x-2)^{2}-(x-1)^{2}-(3-x)(3+x)}{(1-2x)(1+2x)+(1-5x)^{2}-2(4x-1)^{2}-[-2x^{2}-(1-3x)^2]}{(a-1)(a+1)[(3a-1)^2-(2+3a)^2]-18a(2-a^2)-3(1-a)}

$$\left. \begin{array} { l } { ( x - 2 ) ^ { 2 } - ( x - 1 ) ^ { 2 } - ( 3 - x ) ( 3 + x ) } \\ { ( 1 - 2 x ) ( 1 + 2 x ) + ( 1 - 5 x ) ^ { 2 } - 2 ( 4 x - 1 ) ^ { 2 } - [ - 2 x ^ { 2 } - ( 1 - 3 x ) ^ { 2 } ] } \\ { ( a - 1 ) ( a + 1 ) [ ( 3 a - 1 ) ^ { 2 } - ( 2 + 3 a ) ^ { 2 } ] - 18 a ( 2 - a ^ { 2 } ) - 3 ( 1 - a ) } \end{array} \right.$$

Least Common Multiple

$$3a\left(a+5\right)\left(x^{2}-2x-6\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-6-2x+x^{2}=\left(x-\left(\sqrt{7}+1\right)\right)\left(x-\left(-\sqrt{7}+1\right)\right) -15a-3a^{2}=3a\left(-a-5\right)$$

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

$$3a\left(a+5\right)\left(x^{2}-2x-6\right)$$

Expand the expression.

$$3a^{2}x^{2}+15ax^{2}-6xa^{2}-30ax-18a^{2}-90a$$

Evaluate

$$x^{2}-2x-6,\ 1,\ 3a\left(-a-5\right)$$