Solve 2abc^3+2abc^2-50abc-50ab

$$2 a b c ^ { 3 } + 2 a b c ^ { 2 } - 50 a b c - 50 a b$$

Factor

$$2ab\left(c-5\right)\left(c+1\right)\left(c+5\right)$$

Solution Steps

Factor out 2.

$$2\left(abc^{3}+abc^{2}-25abc-25ab\right)$$

Consider abc^{3}+abc^{2}-25abc-25ab. Factor out ab.

$$ab\left(c^{3}+c^{2}-25c-25\right)$$

Consider c^{3}+c^{2}-25c-25. Do the grouping c^{3}+c^{2}-25c-25=\left(c^{3}+c^{2}\right)+\left(-25c-25\right), and factor out c^{2} in the first and -25 in the second group.

$$c^{2}\left(c+1\right)-25\left(c+1\right)$$

Factor out common term c+1 by using distributive property.

$$\left(c+1\right)\left(c^{2}-25\right)$$

Consider c^{2}-25. Rewrite c^{2}-25 as c^{2}-5^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(c-5\right)\left(c+5\right)$$

Rewrite the complete factored expression.

$$2ab\left(c+1\right)\left(c-5\right)\left(c+5\right)$$

Evaluate

$$2ab\left(c+1\right)\left(c^{2}-25\right)$$