What is expand (x+sin((pi*x)/2))*(x+cos((pi*x)/2))^2 ?

The solution to expand (x+sin((pi*x)/2))*(x+cos((pi*x)/2))^2 is

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expand (x+sin((pix)/2))(x+cos((pi*x)/2))^2

expand

(x + sin (\frac{π \cdot x}{2})) \cdot (x + cos (\frac{π \cdot x}{2}))^{2}

x^{3} + 2 x^{2} cos (\frac{π x}{2}) + x cos^{2} (\frac{π x}{2}) + x^{2} sin (\frac{π x}{2}) + 2 x sin (\frac{π x}{2}) cos (\frac{π x}{2}) + cos^{2} (\frac{π x}{2}) sin (\frac{π x}{2})

Solution steps

(x + sin (\frac{π x}{2})) (x + cos (\frac{π x}{2}))^{2}

Apply the distributive law:

a (b + c) = ab + a c

a = (x + cos (\frac{π x}{2}))^{2}, b = x, c = sin (\frac{π x}{2})

= (x + cos (\frac{π x}{2}))^{2} x + (x + cos (\frac{π x}{2}))^{2} sin (\frac{π x}{2})

= x (x + cos (\frac{π x}{2}))^{2} + sin (\frac{π x}{2}) (x + cos (\frac{π x}{2}))^{2}

Simplify

x (x + cos (\frac{π x}{2}))^{2} + sin (\frac{π x}{2}) (x + cos (\frac{π x}{2}))^{2} : x^{3} + 2 x^{2} cos (\frac{π x}{2}) + x cos^{2} (\frac{π x}{2}) + x^{2} sin (\frac{π x}{2}) + 2 x sin (\frac{π x}{2}) cos (\frac{π x}{2}) + cos^{2} (\frac{π x}{2}) sin (\frac{π x}{2})

= x^{3} + 2 x^{2} cos (\frac{π x}{2}) + x cos^{2} (\frac{π x}{2}) + x^{2} sin (\frac{π x}{2}) + 2 x sin (\frac{π x}{2}) cos (\frac{π x}{2}) + cos^{2} (\frac{π x}{2}) sin (\frac{π x}{2})

\frac{10 ( 3 191 - 2 )}{49}

lo g_{10} (y)

\frac{\partial}{\partial x} ((y) (x^{2} + x y - 10))

(3 - 3) (2 + 2)

(4 - 3 x)^{2}

What is expand (x+sin((pi*x)/2))*(x+cos((pi*x)/2))^2 ?
The solution to expand (x+sin((pi*x)/2))*(x+cos((pi*x)/2))^2 is