Solve b^4-2401

$$b ^ { 4 } - 2401$$

Factor

$$\left(b-7\right)\left(b+7\right)\left(b^{2}+49\right)$$

Solution Steps

Rewrite b^{4}-2401 as \left(b^{2}\right)^{2}-49^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(b^{2}-49\right)\left(b^{2}+49\right)$$

Consider b^{2}-49. Rewrite b^{2}-49 as b^{2}-7^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(b-7\right)\left(b+7\right)$$

Rewrite the complete factored expression. Polynomial b^{2}+49 is not factored since it does not have any rational roots.

$$\left(b-7\right)\left(b+7\right)\left(b^{2}+49\right)$$

Evaluate

$$b^{4}-2401$$