Solve 1-y^4

$$1 - y ^ { 4 }$$

Factor

$$\left(y-1\right)\left(y+1\right)\left(-y^{2}-1\right)$$

Solution Steps

Rewrite 1-y^{4} as 1^{2}-\left(-y^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1+y^{2}\right)\left(1-y^{2}\right)$$

Reorder the terms.

$$\left(y^{2}+1\right)\left(-y^{2}+1\right)$$

Consider -y^{2}+1. Rewrite -y^{2}+1 as 1^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-y\right)\left(1+y\right)$$

Reorder the terms.

$$\left(-y+1\right)\left(y+1\right)$$

Rewrite the complete factored expression. Polynomial y^{2}+1 is not factored since it does not have any rational roots.

$$\left(-y+1\right)\left(y+1\right)\left(y^{2}+1\right)$$

Evaluate

$$1-y^{4}$$