Solve {l}{5x_{1}-3x}{2x_{1}+4x_{2}}{x_{1}-11x2}

$$\left. \begin{array} { l } { 5 x _ { 1 } - 3 x } \\ { 2 x _ { 1 } + 4 x _ { 2 } } \\ { x _ { 1 } - 11 x 2 } \end{array} \right.$$

Least Common Multiple

$$2\left(x_{1}-11x_{2}\right)\left(5x_{1}-3x\right)\left(x_{1}+2x_{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$2x_{1}+4x_{2}=2\left(x_{1}+2x_{2}\right)$$

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

$$2\left(x_{1}-11x_{2}\right)\left(5x_{1}-3x\right)\left(x_{1}+2x_{2}\right)$$

Expand the expression.

$$-6xx_{1}^{2}+54xx_{1}x_{2}+132xx_{2}^{2}+10x_{1}^{3}-220x_{1}x_{2}^{2}-90x_{2}x_{1}^{2}$$

Evaluate

$$5x_{1}-3x,\ 2\left(x_{1}+2x_{2}\right),\ x_{1}-11x_{2}$$