What is expand 2aCe^{at}(1+bCe^{at}) ?

The solution to expand 2aCe^{at}(1+bCe^{at}) is 2e^{at}aC+2e^{2at}aC^2b

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expand 2aCe^{at}(1+bCe^{at})

expand

2 a C e^{a t} (1 + b C e^{a t})

2 e^{a t} a C + 2 e^{2 a t} a C^{2} b

Solution steps

2 a C e^{a t} (1 + b C e^{a t})

= 2 e^{a t} a C (1 + e^{a t} C b)

Apply the distributive law:

a (b + c) = ab + a c

a = 2 a C e^{a t}, b = 1, c = b C e^{a t}

= 2 a C e^{a t} \cdot 1 + 2 a C e^{a t} b C e^{a t}

= 2 \cdot 1 \cdot e^{a t} a C + 2 e^{a t} e^{a t} a CC b

Simplify

2 \cdot 1 \cdot e^{a t} a C + 2 e^{a t} e^{a t} a CC b : 2 e^{a t} a C + 2 e^{2 a t} a C^{2} b

= 2 e^{a t} a C + 2 e^{2 a t} a C^{2} b

\frac{2}{( 1.96 ) ^{4}}

(24 x y - 6 x^{2} y - 4 x y^{2}) d x

e^{x} \cdot (1 + e^{- x})^{2}

1 + 6 b - 6

\frac{( x + 1 ) ( x - 2 )}{10}

What is expand 2aCe^{at}(1+bCe^{at}) ?
The solution to expand 2aCe^{at}(1+bCe^{at}) is 2e^{at}aC+2e^{2at}aC^2b