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شائع الجبر >

expand ((2.6)/4 x^pi+(2.2)/(6.8)y^e)^{16}

الحلّ

expand

(\frac{2.6}{4} x^{π} + \frac{2.2}{6.8} y^{e})^{16}

الحلّ

0.00101 \dots x^{16 π} + 0.00808 \dots y^{e} x^{15 π} + 0.03018 \dots x^{14 π} y^{2 e} + 0.07011 \dots x^{13 π} y^{3 e} + 0.11341 \dots x^{12 π} y^{4 e} + 0.13548 \dots x^{11 π} y^{5 e} + 0.12363 \dots x^{10 π} y^{6 e} + 0.08791 \dots x^{9 π} y^{7 e} + 0.04922 \dots x^{8 π} y^{8 e} + 0.02177 \dots x^{7 π} y^{9 e} + 0.00758 \dots x^{6 π} y^{10 e} + 0.00206 \dots x^{5 π} y^{11 e} + 0.00042 \dots x^{4 π} y^{12 e} + 0.00006 \dots x^{3 π} y^{13 e} + 6.97912 E - 6 x^{2 π} y^{14 e} + 4.63169 E - 7 x^{π} y^{15 e} + 1.44086 E - 8 y^{16 e}

خطوات الحلّ

(\frac{2.6}{4} x^{π} + \frac{2.2}{6.8} y^{e})^{16}

\frac{2.6}{4} x^{π} = 0.65 x^{π}

\frac{2.2}{6.8} y^{e} = 0.32352 \dots y^{e}

= (0.65 x^{π} + 0.32352 \dots y^{e})^{16}

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

:فعّل نظريّة ذات الحدّين لنيوتن

a = 0.65 x^{π}, b = 0.32352 \dots y^{e}

= i = 0 \sum 16 (i 16) (0.65 x^{π})^{(16 - i)} (0.32352 \dots y^{e})^{i}

وسّع حاصل الجمع

= \frac{16 !}{0 ! ( 16 - 0 ) !} (0.65 x^{π})^{16} (0.32352 \dots y^{e})^{0} + \frac{16 !}{1 ! ( 16 - 1 ) !} (0.65 x^{π})^{15} (0.32352 \dots y^{e})^{1} + \frac{16 !}{2 ! ( 16 - 2 ) !} (0.65 x^{π})^{14} (0.32352 \dots y^{e})^{2} + \frac{16 !}{3 ! ( 16 - 3 ) !} (0.65 x^{π})^{13} (0.32352 \dots y^{e})^{3} + \frac{16 !}{4 ! ( 16 - 4 ) !} (0.65 x^{π})^{12} (0.32352 \dots y^{e})^{4} + \frac{16 !}{5 ! ( 16 - 5 ) !} (0.65 x^{π})^{11} (0.32352 \dots y^{e})^{5} + \frac{16 !}{6 ! ( 16 - 6 ) !} (0.65 x^{π})^{10} (0.32352 \dots y^{e})^{6} + \frac{16 !}{7 ! ( 16 - 7 ) !} (0.65 x^{π})^{9} (0.32352 \dots y^{e})^{7} + \frac{16 !}{8 ! ( 16 - 8 ) !} (0.65 x^{π})^{8} (0.32352 \dots y^{e})^{8} + \frac{16 !}{9 ! ( 16 - 9 ) !} (0.65 x^{π})^{7} (0.32352 \dots y^{e})^{9} + \frac{16 !}{10 ! ( 16 - 10 ) !} (0.65 x^{π})^{6} (0.32352 \dots y^{e})^{10} + \frac{16 !}{11 ! ( 16 - 11 ) !} (0.65 x^{π})^{5} (0.32352 \dots y^{e})^{11} + \frac{16 !}{12 ! ( 16 - 12 ) !} (0.65 x^{π})^{4} (0.32352 \dots y^{e})^{12} + \frac{16 !}{13 ! ( 16 - 13 ) !} (0.65 x^{π})^{3} (0.32352 \dots y^{e})^{13} + \frac{16 !}{14 ! ( 16 - 14 ) !} (0.65 x^{π})^{2} (0.32352 \dots y^{e})^{14} + \frac{16 !}{15 ! ( 16 - 15 ) !} (0.65 x^{π})^{1} (0.32352 \dots y^{e})^{15} + \frac{16 !}{16 ! ( 16 - 16 ) !} (0.65 x^{π})^{0} (0.32352 \dots y^{e})^{16}

\frac{16 !}{0 ! ( 16 - 0 ) !} (0.65 x^{π})^{16} (0.32352 \dots y^{e})^{0}

بسّط:

0.00101 \dots x^{16 π}

\frac{16 !}{1 ! ( 16 - 1 ) !} (0.65 x^{π})^{15} (0.32352 \dots y^{e})^{1}

بسّط:

0.00808 \dots y^{e} x^{15 π}

\frac{16 !}{2 ! ( 16 - 2 ) !} (0.65 x^{π})^{14} (0.32352 \dots y^{e})^{2}

بسّط:

0.03018 \dots x^{14 π} y^{2 e}

\frac{16 !}{3 ! ( 16 - 3 ) !} (0.65 x^{π})^{13} (0.32352 \dots y^{e})^{3}

بسّط:

0.07011 \dots x^{13 π} y^{3 e}

\frac{16 !}{4 ! ( 16 - 4 ) !} (0.65 x^{π})^{12} (0.32352 \dots y^{e})^{4}

بسّط:

0.11341 \dots x^{12 π} y^{4 e}

\frac{16 !}{5 ! ( 16 - 5 ) !} (0.65 x^{π})^{11} (0.32352 \dots y^{e})^{5}

بسّط:

0.13548 \dots x^{11 π} y^{5 e}

\frac{16 !}{6 ! ( 16 - 6 ) !} (0.65 x^{π})^{10} (0.32352 \dots y^{e})^{6}

بسّط:

0.12363 \dots x^{10 π} y^{6 e}

\frac{16 !}{7 ! ( 16 - 7 ) !} (0.65 x^{π})^{9} (0.32352 \dots y^{e})^{7}

بسّط:

0.08791 \dots x^{9 π} y^{7 e}

\frac{16 !}{8 ! ( 16 - 8 ) !} (0.65 x^{π})^{8} (0.32352 \dots y^{e})^{8}

بسّط:

0.04922 \dots x^{8 π} y^{8 e}

\frac{16 !}{9 ! ( 16 - 9 ) !} (0.65 x^{π})^{7} (0.32352 \dots y^{e})^{9}

بسّط:

0.02177 \dots x^{7 π} y^{9 e}

\frac{16 !}{10 ! ( 16 - 10 ) !} (0.65 x^{π})^{6} (0.32352 \dots y^{e})^{10}

بسّط:

0.00758 \dots x^{6 π} y^{10 e}

\frac{16 !}{11 ! ( 16 - 11 ) !} (0.65 x^{π})^{5} (0.32352 \dots y^{e})^{11}

بسّط:

0.00206 \dots x^{5 π} y^{11 e}

\frac{16 !}{12 ! ( 16 - 12 ) !} (0.65 x^{π})^{4} (0.32352 \dots y^{e})^{12}

بسّط:

0.00042 \dots x^{4 π} y^{12 e}

\frac{16 !}{13 ! ( 16 - 13 ) !} (0.65 x^{π})^{3} (0.32352 \dots y^{e})^{13}

بسّط:

0.00006 \dots x^{3 π} y^{13 e}

\frac{16 !}{14 ! ( 16 - 14 ) !} (0.65 x^{π})^{2} (0.32352 \dots y^{e})^{14}

بسّط:

6.97912 E - 6 x^{2 π} y^{14 e}

\frac{16 !}{15 ! ( 16 - 15 ) !} (0.65 x^{π})^{1} (0.32352 \dots y^{e})^{15}

بسّط:

4.63169 E - 7 x^{π} y^{15 e}

\frac{16 !}{16 ! ( 16 - 16 ) !} (0.65 x^{π})^{0} (0.32352 \dots y^{e})^{16}

بسّط:

1.44086 E - 8 y^{16 e}

= 0.00101 \dots x^{16 π} + 0.00808 \dots y^{e} x^{15 π} + 0.03018 \dots x^{14 π} y^{2 e} + 0.07011 \dots x^{13 π} y^{3 e} + 0.11341 \dots x^{12 π} y^{4 e} + 0.13548 \dots x^{11 π} y^{5 e} + 0.12363 \dots x^{10 π} y^{6 e} + 0.08791 \dots x^{9 π} y^{7 e} + 0.04922 \dots x^{8 π} y^{8 e} + 0.02177 \dots x^{7 π} y^{9 e} + 0.00758 \dots x^{6 π} y^{10 e} + 0.00206 \dots x^{5 π} y^{11 e} + 0.00042 \dots x^{4 π} y^{12 e} + 0.00006 \dots x^{3 π} y^{13 e} + 6.97912 E - 6 x^{2 π} y^{14 e} + 4.63169 E - 7 x^{π} y^{15 e} + 1.44086 E - 8 y^{16 e}

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