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

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

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

expand

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

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

Solution steps

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

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

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

Simplify

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

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

\frac{( 4 x + 9 )}{( x + 3 ) ( x - 3 )}

(2, - 6, 4) x (- 1, 3, 5)

\frac{h ( x + 2 ) - 2 x}{h ( x + 2 )}

det (λ - 1) (λ^{2} - 2 λ - 2)

e^{3 (3 + i)}

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