Solve {l}{(28-3p-12q+5pq-2pq^2+5p^2q)-(4p^2q-3m)}{(0)+5pq^2-8p+7q-10}

$$\left. \begin{array} { l } { ( 28 - 3 p - 12 q + 5 p q - 2 p q ^ { 2 } + 5 p ^ { 2 } q ) - ( 4 p ^ { 2 } q - 3 m ) } \\ { ( 0 ) + 5 p q ^ { 2 } - 8 p + 7 q - 10 } \end{array} \right.$$

Least Common Multiple

$$15mpq^{2}-24mp+21mq-30m-10p^{2}q^{4}+25p^{2}q^{3}+24p^{2}-74pq^{3}+195pq^{2}+25pq-194p-84q^{2}-8qp^{3}-50qp^{2}+316q+5\left(pq\right)^{3}+8\left(pq\right)^{2}-280$$

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.

$$15mpq^{2}-24mp+21mq-30m+5p^{3}q^{3}-10p^{2}q^{4}+25p^{2}q^{3}+8p^{2}q^{2}+24p^{2}-74pq^{3}+195pq^{2}+25pq-194p-84q^{2}-8qp^{3}-50qp^{2}+316q-280$$

Evaluate

$$3m-2pq^{2}+5pq-3p+qp^{2}-12q+28,\ 5pq^{2}-8p+7q-10$$