What is expand (x-pi)*(x^2+2) ?

The solution to expand (x-pi)*(x^2+2) is x^3-pix^2+2x-2pi

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expand (x-pi)*(x^2+2)

expand

(x - π) \cdot (x^{2} + 2)

x^{3} - π x^{2} + 2 x - 2 π

Solution steps

(x - π) (x^{2} + 2)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = x, b = - π, c = x^{2}, d = 2

= x x^{2} + x \cdot 2 + (- π) x^{2} + (- π) \cdot 2

Apply minus-plus rules

+ (- a) = - a

= x^{2} x + 2 x - π x^{2} - 2 π

Simplify

x^{2} x + 2 x - π x^{2} - 2 π : x^{3} - π x^{2} + 2 x - 2 π

= x^{3} - π x^{2} + 2 x - 2 π

x (x - 6 x)

e^{- x} (1 + x) \frac{d y}{d x} - e^{- x} x y

16 n (2 k)^{4} - 32 (2 k)^{3} + 24 (2 k)^{2} - 8 (2 k)

\frac{5 x + 10 - 4 x ^{2}}{x ^{2} ( x + 2 )}

(x + 2) e^{2}

What is expand (x-pi)*(x^2+2) ?
The solution to expand (x-pi)*(x^2+2) is x^3-pix^2+2x-2pi