Solve {l}{(a_{1}+b_{1}x)}{(a_{2}+b_{2}x)}{(a_{3}+b_{3}x_{2})}{(a_{4}+b_{4}x)}

$$\left. \begin{array} { l } { ( a _ { 1 } + b _ { 1 } x ) } \\ { ( a _ { 2 } + b _ { 2 } x ) } \\ { ( a _ { 3 } + b _ { 3 } x _ { 2 } ) } \\ { ( a _ { 4 } + b _ { 4 } x ) } \end{array} \right.$$

Least Common Multiple

$$\left(b_{1}x+a_{1}\right)\left(b_{2}x+a_{2}\right)\left(b_{3}x_{2}+a_{3}\right)\left(b_{4}x+a_{4}\right)$$

Solution Steps

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

$$\left(b_{1}x+a_{1}\right)\left(b_{2}x+a_{2}\right)\left(b_{3}x_{2}+a_{3}\right)\left(b_{4}x+a_{4}\right)$$

Expand the expression.

$$a_{3}b_{1}b_{2}b_{4}x^{3}+a_{1}a_{3}b_{2}b_{4}x^{2}+a_{2}a_{3}b_{1}b_{4}x^{2}+a_{3}a_{4}b_{1}b_{2}x^{2}+a_{1}a_{2}b_{3}b_{4}xx_{2}+a_{1}a_{4}b_{2}b_{3}xx_{2}+a_{2}a_{4}b_{1}b_{3}xx_{2}+a_{1}a_{2}a_{3}b_{4}x+a_{1}a_{3}a_{4}b_{2}x+a_{2}a_{3}a_{4}b_{1}x+b_{1}b_{2}b_{3}b_{4}x_{2}x^{3}+a_{1}b_{2}b_{3}b_{4}x_{2}x^{2}+a_{2}b_{1}b_{3}b_{4}x_{2}x^{2}+a_{4}b_{1}b_{2}b_{3}x_{2}x^{2}+a_{1}a_{2}a_{4}b_{3}x_{2}+a_{1}a_{2}a_{3}a_{4}$$

Evaluate

$$b_{1}x+a_{1},\ b_{2}x+a_{2},\ b_{3}x_{2}+a_{3},\ b_{4}x+a_{4}$$