Solve 50b^4+200b^3-2b^2-8b

$$50 b ^ { 4 } + 200 b ^ { 3 } - 2 b ^ { 2 } - 8 b$$

Factor

$$2b\left(5b-1\right)\left(b+4\right)\left(5b+1\right)$$

Solution Steps

Factor out 2.

$$2\left(25b^{4}+100b^{3}-b^{2}-4b\right)$$

Consider 25b^{4}+100b^{3}-b^{2}-4b. Factor out b.

$$b\left(25b^{3}+100b^{2}-b-4\right)$$

Consider 25b^{3}+100b^{2}-b-4. Do the grouping 25b^{3}+100b^{2}-b-4=\left(25b^{3}+100b^{2}\right)+\left(-b-4\right), and factor out 25b^{2} in the first and -1 in the second group.

$$25b^{2}\left(b+4\right)-\left(b+4\right)$$

Factor out common term b+4 by using distributive property.

$$\left(b+4\right)\left(25b^{2}-1\right)$$

Consider 25b^{2}-1. Rewrite 25b^{2}-1 as \left(5b\right)^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(5b-1\right)\left(5b+1\right)$$

Rewrite the complete factored expression.

$$2b\left(b+4\right)\left(5b-1\right)\left(5b+1\right)$$

Evaluate

$$2b\left(b+4\right)\left(25b^{2}-1\right)$$