expand (10(pi^3+25(pi^2+6)))/(pi^3)

الحلّ

expand

\frac{10 ( π ^{3} + 25 ( π ^{2} + 6 ) )}{π ^{3}}

10 + \frac{250}{π} + \frac{1500}{π ^{3}}

عشري

137.95477 \dots

خطوات الحلّ

\frac{10 ( π ^{3} + 25 ( π ^{2} + 6 ) )}{π ^{3}}

π^{3} + 25 (π^{2} + 6)

وسٌع:

π^{3} + 25 π^{2} + 150

= \frac{10 ( π ^{3} + 25 π ^{2} + 150 )}{π ^{3}}

10 (π^{3} + 25 π^{2} + 150)

وسٌع:

10 π^{3} + 250 π^{2} + 1500

= \frac{10 π ^{3} + 250 π ^{2} + 1500}{π ^{3}}

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

: استخدم ميزات الكسور التالية

\frac{10 π ^{3} + 250 π ^{2} + 1500}{π ^{3}} = \frac{10 π ^{3}}{π ^{3}} + \frac{250 π ^{2}}{π ^{3}} + \frac{1500}{π ^{3}}

= \frac{10 π ^{3}}{π ^{3}} + \frac{250 π ^{2}}{π ^{3}} + \frac{1500}{π ^{3}}

\frac{10 π ^{3}}{π ^{3}}

اختزل:

10

= 10 + \frac{250 π ^{2}}{π ^{3}} + \frac{1500}{π ^{3}}

\frac{250 π ^{2}}{π ^{3}}

اختزل:

\frac{250}{π}

= 10 + \frac{250}{π} + \frac{1500}{π ^{3}}

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