расширить (B+at^2)(pir^2+2picrt+pic^2t^2)

Решение

расширить

(B + a t^{2}) (π r^{2} + 2 π cr t + π c^{2} t^{2})

π B r^{2} + 2 π c Bt r + π c^{2} B t^{2} + πa t^{2} r^{2} + 2 πa c t^{3} r + πa c^{2} t^{4}

Шаги решения

(B + a t^{2}) (π r^{2} + 2 π cr t + π c^{2} t^{2})

= (B + a t^{2}) (π r^{2} + 2 π c t r + π c^{2} t^{2})

Расставьте скобки

= B π r^{2} + B \cdot 2 π cr t + B π c^{2} t^{2} + a t^{2} π r^{2} + a t^{2} \cdot 2 π cr t + a t^{2} π c^{2} t^{2}

= π B r^{2} + 2 π c Bt r + π c^{2} B t^{2} + πa t^{2} r^{2} + 2 πa c t^{2} t r + πa c^{2} t^{2} t^{2}

Упростить

π B r^{2} + 2 π c Bt r + π c^{2} B t^{2} + πa t^{2} r^{2} + 2 πa c t^{2} t r + πa c^{2} t^{2} t^{2} : π B r^{2} + 2 π c Bt r + π c^{2} B t^{2} + πa t^{2} r^{2} + 2 πa c t^{3} r + πa c^{2} t^{4}

= π B r^{2} + 2 π c Bt r + π c^{2} B t^{2} + πa t^{2} r^{2} + 2 πa c t^{3} r + πa c^{2} t^{4}