Solve 2b^4-54b

$$2 { b }^{ 4 } -54b$$

Factor

$$2b\left(b-3\right)\left(b^{2}+3b+9\right)$$

Solution Steps

Factor out 2.

$$2\left(b^{4}-27b\right)$$

Consider b^{4}-27b. Factor out b.

$$b\left(b^{3}-27\right)$$

Consider b^{3}-27. Rewrite b^{3}-27 as b^{3}-3^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

$$\left(b-3\right)\left(b^{2}+3b+9\right)$$

Rewrite the complete factored expression. Polynomial b^{2}+3b+9 is not factored since it does not have any rational roots.

$$2b\left(b-3\right)\left(b^{2}+3b+9\right)$$

Evaluate

$$2b\left(b^{3}-27\right)$$