Solve {l}{4p^2q-3pq+5pq^2-8p+7q-10hbar}{18-3p-11q+5pq-2pq^2+5p^2q}

$$\left. \begin{array} { l } { 4 p ^ { 2 } q - 3 p q + 5 p q ^ { 2 } - 8 p + 7 q - 10 \hbar } \\ { 18 - 3 p - 11 q + 5 p q - 2 p q ^ { 2 } + 5 p ^ { 2 } q } \end{array} \right.$$

Least Common Multiple

$$-10p^{2}q^{4}+31p^{2}q^{3}+24p^{2}-69pq^{3}+20pℏq^{2}+158pq^{2}-50pqℏ+13pq+30pℏ-144p+20q^{2}p^{4}+5q^{2}p^{3}-77q^{2}-52qp^{3}-50qℏp^{2}+41qp^{2}+110qℏ+126q+17\left(pq\right)^{3}-23\left(pq\right)^{2}-180ℏ$$

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.

$$17p^{3}q^{3}-10p^{2}q^{4}+31p^{2}q^{3}-23p^{2}q^{2}+24p^{2}-69pq^{3}+20pℏq^{2}+158pq^{2}-50pqℏ+13pq+30pℏ-144p+20q^{2}p^{4}+5q^{2}p^{3}-77q^{2}-52qp^{3}-50qℏp^{2}+41qp^{2}+110qℏ+126q-180ℏ$$

Evaluate

$$5pq^{2}-3pq-8p+4qp^{2}+7q-10ℏ,\ 18-11q+5qp^{2}-3p+5pq-2pq^{2}$$