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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 2 x, b = e^{x}, c = x^{3}, d = 2 e^{2 x}

= 2 x x^{3} + 2 x \cdot 2 e^{2 x} + e^{x} x^{3} + e^{x} \cdot 2 e^{2 x}

= 2 x^{3} x + 2 \cdot 2 e^{2 x} x + e^{x} x^{3} + 2 e^{x} e^{2 x}

Simplify

2 x^{3} x + 2 \cdot 2 e^{2 x} x + e^{x} x^{3} + 2 e^{x} e^{2 x} : 2 x^{4} + 4 e^{2 x} x + e^{x} x^{3} + 2 e^{3 x}

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

\frac{a}{( a - 1 ) ^{2} ( s - 2 )}

\frac{( x ^{2} - 2 x + 7 )}{x}

x^{3} (x^{3} + \frac{2}{5} - 4 e^{- x})

\frac{( x ^{2} + 7 x + 3 )}{( x ^{2} ( x + 3 ) )}

\frac{E}{s ( R + L s )}

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