Solve -4^4+y^4

$$- 4 ^ { 4 } + y ^ { 4 }$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$y^{4}-256$$

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

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

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

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

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

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

Evaluate

$$y^{4}-256$$

Solution Steps

Calculate 4 to the power of 4 and get 256.

$$-256+y^{4}$$