What is expand (e^{5x}+e^{7x})(e^{8x}-e^{-x}) ?

The solution to expand (e^{5x}+e^{7x})(e^{8x}-e^{-x}) is e^{13x}-e^{4x}+e^{15x}-e^{6x}

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expand (e^{5x}+e^{7x})(e^{8x}-e^{-x})

expand

(e^{5 x} + e^{7 x}) (e^{8 x} - e^{- x})

e^{13 x} - e^{4 x} + e^{15 x} - e^{6 x}

Solution steps

(e^{5 x} + e^{7 x}) (e^{8 x} - e^{- x})

Apply FOIL method:

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

a = e^{5 x}, b = e^{7 x}, c = e^{8 x}, d = - e^{- x}

= e^{5 x} e^{8 x} + e^{5 x} (- e^{- x}) + e^{7 x} e^{8 x} + e^{7 x} (- e^{- x})

Apply minus-plus rules

+ (- a) = - a

= e^{5 x} e^{8 x} - e^{5 x} e^{- x} + e^{7 x} e^{8 x} - e^{7 x} e^{- x}

Simplify

e^{5 x} e^{8 x} - e^{5 x} e^{- x} + e^{7 x} e^{8 x} - e^{7 x} e^{- x} : e^{13 x} - e^{4 x} + e^{15 x} - e^{6 x}

= e^{13 x} - e^{4 x} + e^{15 x} - e^{6 x}

- \frac{1}{s ( s + 5 )}

(x - 1 + 2)^{2}

(0.34 arcsin (\frac{- x + 3.14}{1.35}) + 2.38)^{2}

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

2^{5}

What is expand (e^{5x}+e^{7x})(e^{8x}-e^{-x}) ?
The solution to expand (e^{5x}+e^{7x})(e^{8x}-e^{-x}) is e^{13x}-e^{4x}+e^{15x}-e^{6x}