Solve {l}{a^2-10a+25-ab+5b}{8mp+8np-m^2-2mn-n^2}

$$\left. \begin{array} { l } { a ^ { 2 } - 10 a + 25 - a b + 5 b } \\ { 8 m p + 8 n p - m ^ { 2 } - 2 m n - n ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(5-a\right)\left(a-b-5\right)\left(m+n\right)\left(m+n-8p\right)$$

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.

$$\left(5-a\right)\left(a-b-5\right)\left(m+n\right)\left(m+n-8p\right)$$

Expand the expression.

$$abm^{2}-a^{2}m^{2}+10am^{2}-5bm^{2}-25m^{2}+2abmn-2mna^{2}+20amn-10bmn-50mn+8mpa^{2}-8abmp+40bmp-80amp+200mp+abn^{2}-a^{2}n^{2}+10an^{2}-5bn^{2}-25n^{2}+8npa^{2}-8abnp+40bnp-80anp+200np$$

Evaluate

$$\left(a-5\right)\left(a-b-5\right),\ -\left(m+n\right)\left(m+n-8p\right)$$