What is expand (2e^x+3)^2e^x ?

The solution to expand (2e^x+3)^2e^x is 4e^{3x}+12e^{2x}+9e^x

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expand (2e^x+3)^2e^x

expand

(2 e^{x} + 3)^{2} e^{x}

4 e^{3 x} + 12 e^{2 x} + 9 e^{x}

Solution steps

(2 e^{x} + 3)^{2} e^{x}

(2 e^{x} + 3)^{2} = 4 e^{2 x} + 12 e^{x} + 9

= e^{x} (12 e^{x} + 4 e^{2 x} + 9)

= e^{x} (4 e^{2 x} + 12 e^{x} + 9)

Distribute parentheses

= e^{x} \cdot 4 e^{2 x} + e^{x} \cdot 12 e^{x} + e^{x} \cdot 9

= 4 e^{x} e^{2 x} + 12 e^{x} e^{x} + 9 e^{x}

Simplify

4 e^{x} e^{2 x} + 12 e^{x} e^{x} + 9 e^{x} : 4 e^{3 x} + 12 e^{2 x} + 9 e^{x}

= 4 e^{3 x} + 12 e^{2 x} + 9 e^{x}

{(e^{3 t} + e^{- 3 t}) cos (t)} s

3 (x - 2) - x - 2

cos (x) (2 - 2 sin (x))

(x - 9)^{2} (x - 2 i)^{2}

(1 - 3 x^{2}) \cdot (- α \cdot (2 x - 1) - β \cdot (3 x^{2} - 1) - cos (π x))

What is expand (2e^x+3)^2e^x ?
The solution to expand (2e^x+3)^2e^x is 4e^{3x}+12e^{2x}+9e^x