What is expand (e^x+1)(e^{2x}+e^x-4) ?

The solution to expand (e^x+1)(e^{2x}+e^x-4) is -3e^x+2e^{2x}+e^{3x}-4

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expand (e^x+1)(e^{2x}+e^x-4)

expand

(e^{x} + 1) (e^{2 x} + e^{x} - 4)

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

Solution steps

(e^{x} + 1) (e^{2 x} + e^{x} - 4)

Distribute parentheses

= e^{x} e^{2 x} + e^{x} e^{x} + e^{x} (- 4) + 1 \cdot e^{2 x} + 1 \cdot e^{x} + 1 \cdot (- 4)

Apply minus-plus rules

+ (- a) = - a

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

Simplify

e^{x} e^{2 x} + e^{x} e^{x} - 4 e^{x} + 1 \cdot e^{2 x} + 1 \cdot e^{x} - 1 \cdot 4 : - 3 e^{x} + 2 e^{2 x} + e^{3 x} - 4

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

\frac{( - 2 x + 11 ) ( x - 3 )}{2}

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

\frac{3 u + 2}{6 ( u + 2 )}

7^{^{'}} (5 x + 1) - 10 x

e^{- i θ} (1 + e^{i θ} + e^{2 i θ})

What is expand (e^x+1)(e^{2x}+e^x-4) ?
The solution to expand (e^x+1)(e^{2x}+e^x-4) is -3e^x+2e^{2x}+e^{3x}-4