# Simplify (0.5e^(2t)+e^(2t)+0.5)(e^(-2t)-1)

(0.5e2t+e2t+0.5)(e-2t-1)
(1.5e2t+0.5)(e-2t-1)
Expand (1.5e2t+0.5)(e-2t-1) using the FOIL Method.
Apply the distributive property.
1.5e2t(e-2t-1)+0.5(e-2t-1)
Apply the distributive property.
1.5e2te-2t+1.5e2t⋅-1+0.5(e-2t-1)
Apply the distributive property.
1.5e2te-2t+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
1.5e2te-2t+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
Simplify and combine like terms.
Simplify each term.
Multiply e2t by e-2t by adding the exponents.
Move e-2t.
1.5(e-2te2t)+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
Use the power rule aman=am+n to combine exponents.
1.5e-2t+2t+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
1.5e0+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
1.5e0+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
Simplify 1.5e0.
1.5+1.5e2t⋅-1+0.5e-2t+0.5⋅-1
Multiply -1 by 1.5.
1.5-1.5e2t+0.5e-2t+0.5⋅-1
Multiply 0.5 by -1.
1.5-1.5e2t+0.5e-2t-0.5
1.5-1.5e2t+0.5e-2t-0.5
Subtract 0.5 from 1.5.
1-1.5e2t+0.5e-2t
1-1.5e2t+0.5e-2t
Simplify (0.5e^(2t)+e^(2t)+0.5)(e^(-2t)-1)

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