Solve {l}{1000+8v^6}{144-(x-3)^2}

$$\left. \begin{array} { l } { 1000 + 8 v ^ { 6 } } \\ { 144 - ( x - 3 ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$8\left(x-15\right)\left(x+9\right)\left(v^{6}+125\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$8v^{6}+1000=8\left(v^{2}+5\right)\left(v^{4}-5v^{2}+25\right) 135+6x-x^{2}=\left(x-15\right)\left(-x-9\right)$$

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

$$8\left(x-15\right)\left(x+9\right)\left(v^{2}+5\right)\left(v^{4}-5v^{2}+25\right)$$

Expand the expression.

$$8x^{2}v^{6}+1000x^{2}-48xv^{6}-6000x-1080v^{6}-135000$$

Evaluate

$$8\left(v^{6}+125\right),\ \left(-x-9\right)\left(x-15\right)$$