What is expand [sqrt(t)(t^2+1)+2t^3](2t) ?

The solution to expand [sqrt(t)(t^2+1)+2t^3](2t) is 2t^3sqrt(t)+2tsqrt(t)+4t^4

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expand [sqrt(t)(t^2+1)+2t^3](2t)

expand

[t (t^{2} + 1) + 2 t^{3}] (2 t)

2 t^{3} t + 2 t t + 4 t^{4}

Solution steps

(t (t^{2} + 1) + 2 t^{3}) (2 t)

= (2 t) (t (t^{2} + 1) + 2 t^{3})

Apply the distributive law:

a (b + c) = ab + a c

(2 t) (t (t^{2} + 1) + 2 t^{3}) = 2 t t (t^{2} + 1) + 2 t \cdot 2 t^{3}

= 2 t t (t^{2} + 1) + 2 t \cdot 2 t^{3}

Simplify

2 t \cdot 2 t^{3} : 4 t^{4}

= 2 t t (t^{2} + 1) + 4 t^{4}

Expand

2 t t (t^{2} + 1) : 2 t^{3} t + 2 t t

= 2 t^{3} t + 2 t t + 4 t^{4}

D x [(e^{x} + 4) (x^{2} - \frac{1}{2})]

5 (1 + sin (x))

(3 - 2 s)^{2}

\frac{x ^{2} + 1}{x ( x - 2 )}

(cos^{3} (t) + sin^{3} (t)) \cdot (3 cos (t) sin (t))

What is expand [sqrt(t)(t^2+1)+2t^3](2t) ?
The solution to expand [sqrt(t)(t^2+1)+2t^3](2t) is 2t^3sqrt(t)+2tsqrt(t)+4t^4