What is expand ,(2t+1)u_{1}(t) ?

The solution to expand ,(2t+1)u_{1}(t) is 2t^2u_{1}+tu_{1}

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expand ,(2t+1)u_{1}(t)

expand

(2 t + 1) u_{1} (t)

2 t^{2} u_{1} + t u_{1}

Solution steps

(2 t + 1) u_{1} (t)

Apply rule:

(a) = a

(t) = t

= (2 t + 1) u_{1} t

= t u_{1} (2 t + 1)

Apply the distributive law:

a (b + c) = ab + a c

t u_{1} (2 t + 1) = t u_{1} \cdot 2 t + t u_{1} \cdot 1

= t u_{1} \cdot 2 t + t u_{1} \cdot 1

Simplify

t u_{1} \cdot 2 t + t u_{1} \cdot 1 : 2 t^{2} u_{1} + t u_{1}

= 2 t^{2} u_{1} + t u_{1}

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What is expand ,(2t+1)u_{1}(t) ?
The solution to expand ,(2t+1)u_{1}(t) is 2t^2u_{1}+tu_{1}