Solve {l}{2x^2-35x-18}{8(p-8q)^2-6(p-8)}

$$\left. \begin{array} { l } { 2 x ^ { 2 } - 35 x - 18 } \\ { 8 ( p - 8 q ) ^ { 2 } - 6 ( p - 8 ) } \end{array} \right.$$

Least Common Multiple

$$2\left(x-18\right)\left(2x+1\right)\left(4\left(p-8q\right)^{2}-3p+24\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$8\left(p-8q\right)^{2}-6p+48=2\left(4p^{2}-64pq-3p+256q^{2}+24\right)$$

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

$$2\left(x-18\right)\left(2x+1\right)\left(24-3p+256q^{2}+4p^{2}-64pq\right)$$

Expand the expression.

$$16p^{2}x^{2}+1024q^{2}x^{2}-256pqx^{2}-12px^{2}+96x^{2}+4480pqx-17920xq^{2}-280xp^{2}+210px-1680x+2304pq-9216q^{2}-144p^{2}+108p-864$$

Evaluate

$$\left(x-18\right)\left(2x+1\right),\ 2\left(4\left(p-8q\right)^{2}-3p+24\right)$$