Solve {l}{a^{2}-b^2-20c-c^2}{1-a^2+2ax-x^2}

$$\left. \begin{array} { l } { a ^ { 2 } - b ^ { 2 } - 20 c - c ^ { 2 } } \\ { 1 - a ^ { 2 } + 2 a x - x ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(a^{2}-b^{2}-c^{2}-20c\right)\left(-\left(x-a\right)^{2}+1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$1-\left(a-x\right)^{2}=\left(-x+a-1\right)\left(x-a-1\right)$$

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

$$\left(-x+a-1\right)\left(x-a-1\right)\left(a^{2}-b^{2}-c^{2}-20c\right)$$

Expand the expression.

$$b^{2}x^{2}+c^{2}x^{2}-a^{2}x^{2}+20cx^{2}-2axb^{2}-2axc^{2}+2xa^{3}-40acx+a^{2}b^{2}+a^{2}c^{2}-a^{4}+20ca^{2}-b^{2}-c^{2}+a^{2}-20c$$

Evaluate

$$a^{2}-b^{2}-c^{2}-20c,\ -\left(a-x\right)^{2}+1$$