What is expand t^2e^{4t^5}(3-20t^5-40t^2) ?

The solution to expand t^2e^{4t^5}(3-20t^5-40t^2) is 3e^{4t^5}t^2-20e^{4t^5}t^7-40e^{4t^5}t^4

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expand t^2e^{4t^5}(3-20t^5-40t^2)

expand

t^{2} e^{4 t^{5}} (3 - 20 t^{5} - 40 t^{2})

3 e^{4 t^{5}} t^{2} - 20 e^{4 t^{5}} t^{7} - 40 e^{4 t^{5}} t^{4}

Solution steps

t^{2} e^{4 t^{5}} (3 - 20 t^{5} - 40 t^{2})

= e^{4 t^{5}} t^{2} (3 - 20 t^{5} - 40 t^{2})

Distribute parentheses

= t^{2} e^{4 t^{5}} \cdot 3 + t^{2} e^{4 t^{5}} (- 20 t^{5}) + t^{2} e^{4 t^{5}} (- 40 t^{2})

Apply minus-plus rules

+ (- a) = - a

= 3 e^{4 t^{5}} t^{2} - 20 e^{4 t^{5}} t^{5} t^{2} - 40 e^{4 t^{5}} t^{2} t^{2}

Simplify

3 e^{4 t^{5}} t^{2} - 20 e^{4 t^{5}} t^{5} t^{2} - 40 e^{4 t^{5}} t^{2} t^{2} : 3 e^{4 t^{5}} t^{2} - 20 e^{4 t^{5}} t^{7} - 40 e^{4 t^{5}} t^{4}

= 3 e^{4 t^{5}} t^{2} - 20 e^{4 t^{5}} t^{7} - 40 e^{4 t^{5}} t^{4}

8 (sin (2 x) - cos (2 x))

l im x \Rightarrow - 1 (x^{3} - 2 x^{2} - 5 x - 1)

11 (10 + 2)

π (1 + \frac{3}{5})

y^{''} (x) - (x + 1) y

What is expand t^2e^{4t^5}(3-20t^5-40t^2) ?
The solution to expand t^2e^{4t^5}(3-20t^5-40t^2) is 3e^{4t^5}t^2-20e^{4t^5}t^7-40e^{4t^5}t^4