What is expand (u^5(t)(t-5)-u^{10}(t)(t-10))/5 ?

The solution to expand (u^5(t)(t-5)-u^{10}(t)(t-10))/5 is (u^5t^2)/5-u^5t-(u^{10}t^2)/5+2u^{10}t

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expand (u^5(t)(t-5)-u^{10}(t)(t-10))/5

expand

\frac{u ^{5} ( t ) ( t - 5 ) - u ^{10} ( t ) ( t - 10 )}{5}

\frac{u ^{5} t ^{2}}{5} - u^{5} t - \frac{u ^{10} t ^{2}}{5} + 2 u^{10} t

Solution steps

\frac{u ^{5} ( t ) ( t - 5 ) - u ^{10} ( t ) ( t - 10 )}{5}

Remove parentheses:

(a) = a

= \frac{u ^{5} t ( t - 5 ) - u ^{10} t ( t - 10 )}{5}

Expand

u^{5} t (t - 5) - u^{10} t (t - 10) : u^{5} t^{2} - 5 u^{5} t - u^{10} t^{2} + 10 u^{10} t

= \frac{u ^{5} t ^{2} - 5 u ^{5} t - u ^{10} t ^{2} + 10 u ^{10} t}{5}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{u ^{5} t ^{2} - 5 u ^{5} t - u ^{10} t ^{2} + 10 u ^{10} t}{5} = \frac{u ^{5} t ^{2}}{5} - \frac{5 u ^{5} t}{5} - \frac{u ^{10} t ^{2}}{5} + \frac{10 u ^{10} t}{5}

= \frac{u ^{5} t ^{2}}{5} - \frac{5 u ^{5} t}{5} - \frac{u ^{10} t ^{2}}{5} + \frac{10 u ^{10} t}{5}

Divide the numbers:

\frac{5}{5} = 1

= \frac{u ^{5} t ^{2}}{5} - u^{5} t - \frac{u ^{10} t ^{2}}{5} + \frac{10 u ^{10} t}{5}

Divide the numbers:

\frac{10}{5} = 2

= \frac{u ^{5} t ^{2}}{5} - u^{5} t - \frac{u ^{10} t ^{2}}{5} + 2 u^{10} t

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What is expand (u^5(t)(t-5)-u^{10}(t)(t-10))/5 ?
The solution to expand (u^5(t)(t-5)-u^{10}(t)(t-10))/5 is (u^5t^2)/5-u^5t-(u^{10}t^2)/5+2u^{10}t