Solve 2t^2-2t^6

$$2 t ^ { 2 } - 2 t ^ { 6 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(t^{2}-t^{6}\right)$$

Consider t^{2}-t^{6}. Factor out t^{2}.

$$t^{2}\left(1-t^{4}\right)$$

Consider 1-t^{4}. Rewrite 1-t^{4} as 1^{2}-\left(-t^{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).

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

Reorder the terms.

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

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

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

Reorder the terms.

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

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

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

Evaluate

$$2t^{2}-2t^{6}$$