What is expand (x^2)(x^3-5e^{-2x}-2x^{1/2}) ?

The solution to expand (x^2)(x^3-5e^{-2x}-2x^{1/2}) is x^5-5e^{-2x}x^2-2x^{5/2}

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expand (x^2)(x^3-5e^{-2x}-2x^{1/2})

expand

(x^{2}) (x^{3} - 5 e^{- 2 x} - 2 x^{\frac{1}{2}})

x^{5} - 5 e^{- 2 x} x^{2} - 2 x^{\frac{5}{2}}

Solution steps

(x^{2}) (x^{3} - 5 e^{- 2 x} - 2 x^{\frac{1}{2}})

Distribute parentheses

= (x^{2}) x^{3} + (x^{2}) (- 5 e^{- 2 x}) + (x^{2}) (- 2 x^{\frac{1}{2}})

Apply minus-plus rules

+ (- a) = - a

= x^{3} (x^{2}) - 5 e^{- 2 x} (x^{2}) - 2 x^{\frac{1}{2}} (x^{2})

Simplify

x^{3} (x^{2}) - 5 e^{- 2 x} (x^{2}) - 2 x^{\frac{1}{2}} (x^{2}) : x^{5} - 5 e^{- 2 x} x^{2} - 2 x^{\frac{5}{2}}

= x^{5} - 5 e^{- 2 x} x^{2} - 2 x^{\frac{5}{2}}

(1 + a) (1 - a)

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

- \frac{10 ( x + 4 )}{9}

A (- 1, - 2) y B (- 2, 2)

(x + 6 + x + 1)^{2}

What is expand (x^2)(x^3-5e^{-2x}-2x^{1/2}) ?
The solution to expand (x^2)(x^3-5e^{-2x}-2x^{1/2}) is x^5-5e^{-2x}x^2-2x^{5/2}