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}

\frac{- 17 x - 36}{( x + 1 ) ( 5 x + 9 )}

(4, - 3) y (1, 3)

(x - 4) \cdot (x^{2} - 4)

x^{2} + (y - 3)^{2}

\frac{x - 2}{( x + 9 ) ( x - 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}