Solve 2b^4-32

$$2 b ^ { 4 } - 32$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(b^{4}-16\right)$$

Consider b^{4}-16. Rewrite b^{4}-16 as \left(b^{2}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Consider b^{2}-4. Rewrite b^{2}-4 as b^{2}-2^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(b-2\right)\left(b+2\right)$$

Rewrite the complete factored expression. Polynomial b^{2}+4 is not factored since it does not have any rational roots.

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

Evaluate

$$2\left(b^{4}-16\right)$$