What is expand-(5m(t+10s)^2)/(s^2) ?

The solution to expand-(5m(t+10s)^2)/(s^2) is -(5mt^2}{s^2}-\frac{100mt)/s-500m

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expand-(5m(t+10s)^2)/(s^2)

expand

- \frac{5 m ( t + 10 s ) ^{2}}{s ^{2}}

- \frac{5 m t ^{2}}{s ^{2}} - \frac{100 m t}{s} - 500 m

Solution steps

- \frac{5 m ( t + 10 s ) ^{2}}{s ^{2}}

(t + 10 s)^{2} = t^{2} + 20 t s + 100 s^{2}

= - \frac{5 m ( t ^{2} + 20 t s + 100 s ^{2} )}{s ^{2}}

Expand

5 m (t^{2} + 20 t s + 100 s^{2}) : 5 m t^{2} + 100 m t s + 500 m s^{2}

= - \frac{5 m t ^{2} + 100 m t s + 500 m s ^{2}}{s ^{2}}

Apply the fraction rule:

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

\frac{5 m t ^{2} + 100 m t s + 500 m s ^{2}}{s ^{2}} = - (\frac{5 m t ^{2}}{s ^{2}}) - (\frac{100 m t s}{s ^{2}}) - (\frac{500 m s ^{2}}{s ^{2}})

= - (\frac{5 m t ^{2}}{s ^{2}}) - (\frac{100 m t s}{s ^{2}}) - (\frac{500 m s ^{2}}{s ^{2}})

Remove parentheses:

(a) = a

= - \frac{5 m t ^{2}}{s ^{2}} - \frac{100 m t s}{s ^{2}} - \frac{500 m s ^{2}}{s ^{2}}

Cancel

\frac{100 m t s}{s ^{2}} : \frac{100 m t}{s}

= - \frac{5 m t ^{2}}{s ^{2}} - \frac{100 m t}{s} - \frac{500 m s ^{2}}{s ^{2}}

Cancel

\frac{500 m s ^{2}}{s ^{2}} : 500 m

= - \frac{5 m t ^{2}}{s ^{2}} - \frac{100 m t}{s} - 500 m

\frac{5 x}{( x + 3 ) ^{4}}

2^{2} - 2

\frac{12 ( 1 - cos ( x ) )}{x ^{2}}

u \cdot (1 - e^{- x})

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

What is expand-(5m(t+10s)^2)/(s^2) ?
The solution to expand-(5m(t+10s)^2)/(s^2) is -(5mt^2}{s^2}-\frac{100mt)/s-500m