What is expand 10(-2e^{-2x}cos^2(x)-e^{-2x}sin(2x)) ?

The solution to expand 10(-2e^{-2x}cos^2(x)-e^{-2x}sin(2x)) is -20e^{-2x}cos^2(x)-10e^{-2x}sin(2x)

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expand 10(-2e^{-2x}cos^2(x)-e^{-2x}sin(2x))

expand

10 (- 2 e^{- 2 x} cos^{2} (x) - e^{- 2 x} sin (2 x))

- 20 e^{- 2 x} cos^{2} (x) - 10 e^{- 2 x} sin (2 x)

Solution steps

10 (- 2 e^{- 2 x} cos^{2} (x) - e^{- 2 x} sin (2 x))

Apply the distributive law:

a (b - c) = ab - a c

a = 10, b = - 2 e^{- 2 x} cos^{2} (x), c = e^{- 2 x} sin (2 x)

= 10 (- 2 e^{- 2 x} cos^{2} (x)) - 10 e^{- 2 x} sin (2 x)

Apply minus-plus rules

+ (- a) = - a

= - 10 \cdot 2 e^{- 2 x} cos^{2} (x) - 10 e^{- 2 x} sin (2 x)

Multiply the numbers:

10 \cdot 2 = 20

= - 20 e^{- 2 x} cos^{2} (x) - 10 e^{- 2 x} sin (2 x)

(x + δ x)^{2}

(x + δ x)^{5}

(x + δ x)^{4}

(x^{2} + 1)^{\circ} (x - 3)

lo g_{6} (x) (x - 1)^{2}

What is expand 10(-2e^{-2x}cos^2(x)-e^{-2x}sin(2x)) ?
The solution to expand 10(-2e^{-2x}cos^2(x)-e^{-2x}sin(2x)) is -20e^{-2x}cos^2(x)-10e^{-2x}sin(2x)