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

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

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expand (e^{3x}-1)(e^{-x}+4)

expand

(e^{3 x} - 1) (e^{- x} + 4)

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

Solution steps

(e^{3 x} - 1) (e^{- x} + 4)

Apply FOIL method:

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

a = e^{3 x}, b = - 1, c = e^{- x}, d = 4

= e^{3 x} e^{- x} + e^{3 x} \cdot 4 + (- 1) e^{- x} + (- 1) \cdot 4

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

(- 25 π x + 4)^{2}

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

(x - y)^{2} + (n - m)^{2}

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

c u r l (a y + 2 x a y, a x + a x, 0)

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