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

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

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expand (Ae^t-Be^{-t})^2

expand

(A e^{t} - B e^{- t})^{2}

A^{2} e^{2 t} - 2 A B + B^{2} e^{- 2 t}

Solution steps

(A e^{t} - B e^{- t})^{2}

Apply Perfect Square Formula:

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

a = A e^{t}, b = B e^{- t}

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

Simplify

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

= A^{2} e^{2 t} - 2 A B + B^{2} e^{- 2 t}

A (5, - 5) Y B (8, 3)

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2.5 sin (2.5 (x - 8.5))

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