расширить ((t+c)^2)/(10000pi^2)

Решение

расширить

\frac{( t + c ) ^{2}}{10000 π ^{2}}

\frac{t ^{2}}{10000 π ^{2}} + \frac{c t}{5000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

Шаги решения

\frac{( t + c ) ^{2}}{10000 π ^{2}}

(t + c)^{2} = t^{2} + 2 c t + c^{2}

= \frac{t ^{2} + 2 c t + c ^{2}}{10000 π ^{2}}

Примените правило дробей:

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

\frac{t ^{2} + 2 t c + c ^{2}}{10000 π ^{2}} = \frac{t ^{2}}{10000 π ^{2}} + \frac{2 t c}{10000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

= \frac{t ^{2}}{10000 π ^{2}} + \frac{2 c t}{10000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}

Упраздните

\frac{2 t c}{10000 π ^{2}} : \frac{c t}{5000 π ^{2}}

= \frac{t ^{2}}{10000 π ^{2}} + \frac{c t}{5000 π ^{2}} + \frac{c ^{2}}{10000 π ^{2}}