Factor e^(2t)+2e^t+1

Math
e2t+2et+1
Rewrite e2t as (et)2.
(et)2+2et+1
Let u=et. Substitute u for all occurrences of et.
u2+2u+1
Factor using the perfect square rule.
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Rewrite 1 as 12.
u2+2u+12
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
2u=2⋅u⋅1
Rewrite the polynomial.
u2+2⋅u⋅1+12
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=u and b=1.
(u+1)2
(u+1)2
Replace all occurrences of u with et.
(et+1)2
Factor e^(2t)+2e^t+1

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