What is expand (x^2+2x)((2x+2)e^{x^2+2x}) ?

The solution to expand (x^2+2x)((2x+2)e^{x^2+2x}) is 2e^{x^2+2x}x^3+6e^{x^2+2x}x^2+4e^{x^2+2x}x

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expand (x^2+2x)((2x+2)e^{x^2+2x})

expand

(x^{2} + 2 x) ((2 x + 2) e^{x^{2} + 2 x})

2 e^{x^{2} + 2 x} x^{3} + 6 e^{x^{2} + 2 x} x^{2} + 4 e^{x^{2} + 2 x} x

Solution steps

(x^{2} + 2 x) ((2 x + 2) e^{x^{2} + 2 x})

= (x^{2} + 2 x) (e^{x^{2} + 2 x} (2 x + 2))

Apply the distributive law:

a (b + c) = ab + a c

a = ((2 x + 2) e^{x^{2} + 2 x}), b = x^{2}, c = 2 x

= ((2 x + 2) e^{x^{2} + 2 x}) x^{2} + ((2 x + 2) e^{x^{2} + 2 x}) \cdot 2 x

= x^{2} (e^{x^{2} + 2 x} (2 x + 2)) + 2 x (e^{x^{2} + 2 x} (2 x + 2))

Simplify

x^{2} (e^{x^{2} + 2 x} (2 x + 2)) + 2 x (e^{x^{2} + 2 x} (2 x + 2)) : 2 e^{x^{2} + 2 x} x^{3} + 6 e^{x^{2} + 2 x} x^{2} + 4 e^{x^{2} + 2 x} x

= 2 e^{x^{2} + 2 x} x^{3} + 6 e^{x^{2} + 2 x} x^{2} + 4 e^{x^{2} + 2 x} x

(sin (θ) + cos (θ)) (sin (x) - cos (x))

(x + 2) sin (x^{2} + 4 x + 17)

(1 - 2 cos (x) + cos (2 x))^{2}

(tan^{(2)} (y) - cot^{(2)} (y))^{(2)}

What is expand (x^2+2x)((2x+2)e^{x^2+2x}) ?
The solution to expand (x^2+2x)((2x+2)e^{x^2+2x}) is 2e^{x^2+2x}x^3+6e^{x^2+2x}x^2+4e^{x^2+2x}x