What is expand (ae^x-be^{-x})^2 ?

The solution to expand (ae^x-be^{-x})^2 is e^{2x}a^2-2ab+e^{-2x}b^2

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expand (ae^x-be^{-x})^2

expand

(a e^{x} - b e^{- x})^{2}

e^{2 x} a^{2} - 2 ab + e^{- 2 x} b^{2}

Solution steps

(a e^{x} - b e^{- x})^{2}

= (e^{x} a - e^{- x} b)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = a e^{x}, b = b e^{- x}

= (a e^{x})^{2} - 2 a e^{x} b e^{- x} + (b e^{- x})^{2}

Simplify

(a e^{x})^{2} - 2 a e^{x} b e^{- x} + (b e^{- x})^{2} : e^{2 x} a^{2} - 2 ab + e^{- 2 x} b^{2}

= e^{2 x} a^{2} - 2 ab + e^{- 2 x} b^{2}

- 3 x (c_{1} (2 x ln (x) + x))

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

e^{((- 3 + 5 \cdot I) \cdot x)}

\frac{2 ( ab + a c + b c )}{ab c}

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

What is expand (ae^x-be^{-x})^2 ?
The solution to expand (ae^x-be^{-x})^2 is e^{2x}a^2-2ab+e^{-2x}b^2