What is expand (3ce^{3x}-5de^{-5x})^2 ?

The solution to expand (3ce^{3x}-5de^{-5x})^2 is 9c^2e^{6x}-30cde^{-2x}+25d^2e^{-10x}

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expand (3ce^{3x}-5de^{-5x})^2

expand

(3 c e^{3 x} - 5 d e^{- 5 x})^{2}

9 c^{2} e^{6 x} - 30 c d e^{- 2 x} + 25 d^{2} e^{- 10 x}

Solution steps

(3 c e^{3 x} - 5 d e^{- 5 x})^{2}

Apply Perfect Square Formula:

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

a = 3 c e^{3 x}, b = 5 d e^{- 5 x}

= (3 c e^{3 x})^{2} - 2 \cdot 3 c e^{3 x} \cdot 5 d e^{- 5 x} + (5 d e^{- 5 x})^{2}

Simplify

(3 c e^{3 x})^{2} - 2 \cdot 3 c e^{3 x} \cdot 5 d e^{- 5 x} + (5 d e^{- 5 x})^{2} : 9 c^{2} e^{6 x} - 30 c d e^{- 2 x} + 25 d^{2} e^{- 10 x}

= 9 c^{2} e^{6 x} - 30 c d e^{- 2 x} + 25 d^{2} e^{- 10 x}

(a + b + c + d + 1)^{3}

\frac{3 x ^{2} - 4 x - 3}{( 3 x - 2 ) ^{2}}

(cos (x + 2 y)) (1 + \frac{2 d y}{d x})

\frac{1}{( n - 1 ) ! ( n + 1 )}

d x (3 x^{3} + cos (x))

What is expand (3ce^{3x}-5de^{-5x})^2 ?
The solution to expand (3ce^{3x}-5de^{-5x})^2 is 9c^2e^{6x}-30cde^{-2x}+25d^2e^{-10x}