What is expand (Ae^{-kx}+Be^{kx})^2 ?

The solution to expand (Ae^{-kx}+Be^{kx})^2 is A^2e^{-2kx}+2AB+B^2e^{2kx}

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expand (Ae^{-kx}+Be^{kx})^2

expand

(A e^{- k x} + B e^{k x})^{2}

A^{2} e^{- 2 k x} + 2 A B + B^{2} e^{2 k x}

Solution steps

(A e^{- k x} + B e^{k x})^{2}

Apply Perfect Square Formula:

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

a = A e^{- k x}, b = B e^{k x}

= (A e^{- k x})^{2} + 2 A e^{- k x} B e^{k x} + (B e^{k x})^{2}

Simplify

(A e^{- k x})^{2} + 2 A e^{- k x} B e^{k x} + (B e^{k x})^{2} : A^{2} e^{- 2 k x} + 2 A B + B^{2} e^{2 k x}

= A^{2} e^{- 2 k x} + 2 A B + B^{2} e^{2 k x}

im x \Rightarrow - 2 (x^{3} + 8 x + 2)

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

What is expand (Ae^{-kx}+Be^{kx})^2 ?
The solution to expand (Ae^{-kx}+Be^{kx})^2 is A^2e^{-2kx}+2AB+B^2e^{2kx}