What is expand (x+1)(e^x+e^xx) ?

The solution to expand (x+1)(e^x+e^xx) is 2e^xx+e^xx^2+e^x

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expand (x+1)(e^x+e^xx)

expand

(x + 1) (e^{x} + e^{x} x)

2 e^{x} x + e^{x} x^{2} + e^{x}

Solution steps

(x + 1) (e^{x} + e^{x} x)

Apply FOIL method:

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

a = x, b = 1, c = e^{x}, d = e^{x} x

= x e^{x} + x e^{x} x + 1 \cdot e^{x} + 1 \cdot e^{x} x

= e^{x} x + e^{x} xx + 1 \cdot e^{x} + 1 \cdot e^{x} x

Simplify

e^{x} x + e^{x} xx + 1 \cdot e^{x} + 1 \cdot e^{x} x : 2 e^{x} x + e^{x} x^{2} + e^{x}

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

h (1 - \frac{v ^{2} t ^{2}}{b ^{2}})

\frac{s ^{3}}{( π ^{2} + s ^{2} ) ( s - φ )}

δ (x - 40 π)

(1 + x^{\frac{3}{4}}) (1 - x^{\frac{2}{3}})

What is expand (x+1)(e^x+e^xx) ?
The solution to expand (x+1)(e^x+e^xx) is 2e^xx+e^xx^2+e^x