What is expand (1+e^x)(6-xe^x) ?

The solution to expand (1+e^x)(6-xe^x) is 6-e^xx+6e^x-e^{2x}x

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expand (1+e^x)(6-xe^x)

expand

(1 + e^{x}) (6 - x e^{x})

6 - e^{x} x + 6 e^{x} - e^{2 x} x

Solution steps

(1 + e^{x}) (6 - x e^{x})

= (1 + e^{x}) (6 - e^{x} x)

Apply FOIL method:

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

a = 1, b = e^{x}, c = 6, d = - x e^{x}

= 1 \cdot 6 + 1 \cdot (- x e^{x}) + e^{x} \cdot 6 + e^{x} (- x e^{x})

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot 6 - 1 \cdot e^{x} x + 6 e^{x} - e^{x} e^{x} x

Simplify

1 \cdot 6 - 1 \cdot e^{x} x + 6 e^{x} - e^{x} e^{x} x : 6 - e^{x} x + 6 e^{x} - e^{2 x} x

= 6 - e^{x} x + 6 e^{x} - e^{2 x} x

\frac{x + 1}{( x + 0.2 ) ( x + 0.8 )}

\frac{( x + 2 ) ( x - 2 )}{( x - 4 )}

2 x^{2} + 8 x + 8 + 2 x^{2} + 8 x + 8 + 4 x + 8 + 4 x + 8

(x - y + 2) d x - d y

\frac{1}{s ^{2} - s + 2} \cdot \frac{12 ( 2 s - 1 )}{s + 1}

What is expand (1+e^x)(6-xe^x) ?
The solution to expand (1+e^x)(6-xe^x) is 6-e^xx+6e^x-e^{2x}x