Solve 27w^5-75w

$$27 w ^ { 5 } - 75 w$$

Factor

$$3w\left(3w^{2}-5\right)\left(3w^{2}+5\right)$$

Solution Steps

Factor out 3.

$$3\left(9w^{5}-25w\right)$$

Consider 9w^{5}-25w. Factor out w.

$$w\left(9w^{4}-25\right)$$

Consider 9w^{4}-25. Rewrite 9w^{4}-25 as \left(3w^{2}\right)^{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).

$$\left(3w^{2}-5\right)\left(3w^{2}+5\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: 3w^{2}-5,3w^{2}+5.

$$3w\left(3w^{2}-5\right)\left(3w^{2}+5\right)$$

Evaluate

$$27w^{5}-75w$$