What is expand (1+x)^4*e^x ?

The solution to expand (1+x)^4*e^x is e^x+4e^xx+6e^xx^2+4e^xx^3+e^xx^4

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expand (1+x)^4*e^x

expand

(1 + x)^{4} \cdot e^{x}

e^{x} + 4 e^{x} x + 6 e^{x} x^{2} + 4 e^{x} x^{3} + e^{x} x^{4}

Solution steps

(1 + x)^{4} e^{x}

(1 + x)^{4} = 1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4}

= e^{x} (x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1)

= e^{x} (1 + 4 x + 6 x^{2} + 4 x^{3} + x^{4})

Distribute parentheses

= e^{x} \cdot 1 + e^{x} \cdot 4 x + e^{x} \cdot 6 x^{2} + e^{x} \cdot 4 x^{3} + e^{x} x^{4}

= 1 \cdot e^{x} + 4 e^{x} x + 6 e^{x} x^{2} + 4 e^{x} x^{3} + e^{x} x^{4}

Multiply:

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

= e^{x} + 4 e^{x} x + 6 e^{x} x^{2} + 4 e^{x} x^{3} + e^{x} x^{4}

64 sin (θ) + 64 cos (θ) sin (θ)

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\frac{\partial}{\partial x} ((u (x, y)) (x - y))

\frac{( 100 \cdot ( s + 25 ) )}{( s \cdot ( s + 5 ) ^{3} )}

\frac{\partial}{\partial x} ((y) (x^{4} + y^{4}))

What is expand (1+x)^4*e^x ?
The solution to expand (1+x)^4*e^x is e^x+4e^xx+6e^xx^2+4e^xx^3+e^xx^4