Алгебра. Задание 21.. Created by Miа16. algebra-ru

Алгебра. Задание 21...

Miа16 @Miа16

August 2022 1 40 Report

Алгебра.

Задание 21.

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$1)(2-3x)^{5}=2^{5}-5*2^{4}*3x+10*2^{3}*(3x)^{2}-10*2^{2}*(3x)^{3}+5*2*(3x)^{4}-(3x)^{5}=\\\\=32-240x+720x^{2}-1080x^{3}+810x^{4}-405x^{5} \\\\2)(1+2x)^{7}=1^{7}+7*1^{6}*2x+21*1^{5}*(2x)^{2}+35*1^{4}*(2x)^{3}+35*1^{3} *(2x)^{4} +\\\\+21*1^{2}*(2x)^{5}+7*1*(2x)^{6}+(2x)^{7}=\\\\=1+14x+84x^{2}+280x^{3}+560x^{4}+672x^{5} +448x^{6}+128x^{7}\\\\3)(3+2x^{3})^{9}=3^{9}+9*3^{8}*2x^{3}+36*3^{7} *(2x^{3})^{2}+84*3^{6}* (2x^{3} )^{3}+126* 3^{5}*(2x^{3})^{4}+$

$+126*3^{4}*(2x^{3})^{5}+84*3^{3}*(2x^{3})^{6}+36*3^{2} *(2x^{3})^{7}+9*3*(2x^{3})^{8}+(2x^{3})^{9}=\\\\=19683+118098x^{3} +314928x^{6}+489888x^{9}+489888x^{12}+326592x^{15}+\\\\+145152x^{18}+41472x^{21}+6912x^{24}+512x^{27}\\\\\\4)x(2-3x)^{5}+x^{3}(1+2x^{2})^{7}=32x-240x^{2}+720x^{3} -1080x^{4}+810x^{5}-405x^{6}+\\\\+x^{3}+14x^{4}+84x^{5}+280x^{6}+560x^{7} +672x^{8}+448x^{9}+128x^{10}=$

$=32x-240x^{2}+721x^{3} -1066 x^{4}+894x^{5}-125x^{6}+560x^{7} +672x^{8} +448x^{9} +\\\\+128x^{10}\\\\Otvet:\boxed{894}$

Последнее можно не вычитать, так как там нет нужного одночлена.

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