Solve 256-b^4

$$256 - b ^ { 4 }$$

Factor

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

Solution Steps

Rewrite 256-b^{4} as 16^{2}-\left(-b^{2}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Reorder the terms.

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

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

$$\left(4-b\right)\left(4+b\right)$$

Reorder the terms.

$$\left(-b+4\right)\left(b+4\right)$$

Rewrite the complete factored expression. Polynomial b^{2}+16 is not factored since it does not have any rational roots.

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

Evaluate

$$256-b^{4}$$