Solve {l}{49c^{2}-14c+1-21ac+3a}{ax^{2}+au^{2}+x^4+2x^2u^2+u^4}

$$\left. \begin{array} { l } { 49 c ^ { 2 } - 14 c + 1 - 21 a c + 3 a } \\ { a x ^ { 2 } + a u ^ { 2 } + x ^ { 4 } + 2 x ^ { 2 } u ^ { 2 } + u ^ { 4 } } \end{array} \right.$$

Least Common Multiple

$$\left(7c-1\right)\left(3a-7c+1\right)\left(x^{2}+u^{2}\right)\left(x^{2}+u^{2}+a\right)$$

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.

$$\left(7c-1\right)\left(3a-7c+1\right)\left(x^{2}+u^{2}\right)\left(x^{2}+u^{2}+a\right)$$

Expand the expression.

$$21acx^{4}-49c^{2}x^{4}+14cx^{4}-3ax^{4}-x^{4}+42acu^{2}x^{2}-98c^{2}u^{2}x^{2}+21ca^{2}x^{2}+28cu^{2}x^{2}-49ac^{2}x^{2}-6au^{2}x^{2}+14acx^{2}-3a^{2}x^{2}-2u^{2}x^{2}-ax^{2}+21acu^{4}-49c^{2}u^{4}+21ca^{2}u^{2}-49ac^{2}u^{2}+14cu^{4}-3au^{4}+14acu^{2}-3a^{2}u^{2}-u^{4}-au^{2}$$

Evaluate

$$\left(1-7c\right)\left(3a-7c+1\right),\ \left(x^{2}+u^{2}\right)\left(x^{2}+u^{2}+a\right)$$