Solve 2m^3+m^2-50m-25

$$2 m ^ { 3 } + m ^ { 2 } - 50 m - 25$$

Factor

$$\left(m-5\right)\left(m+5\right)\left(2m+1\right)$$

Solution Steps

Do the grouping 2m^{3}+m^{2}-50m-25=\left(2m^{3}+m^{2}\right)+\left(-50m-25\right), and factor out m^{2} in the first and -25 in the second group.

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

Factor out common term 2m+1 by using distributive property.

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

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

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

Rewrite the complete factored expression.

$$\left(m-5\right)\left(2m+1\right)\left(m+5\right)$$

Evaluate

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