Question

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Answer 1

Ответ:

Объяснение:

воспользуемся формулой

разности квадратов:    a²-b²=(a-b)(a+b)

$\displaystyle\bf\\\frac{17,5^2-9,5^2}{131,5^2-3,5^2} =\frac{(17,5-9,5)(17,5+9,5)}{(131,5-3,5)(141,5+3,5)} =\\\\=\frac{8\cdot27}{128\cdot135} =\frac{8\cdot27}{8\cdot16\cdot5\cdot27}=\frac{1}{80} =0,0125 \\\\\\84\cdot76=(80+4)(80-4)=80^2-4^2=6400-16=6384$

$\displaystyle\bf\\81a^{14}-100b^{18}=(9a^7)^2-(10b^9)^2=\\\\=(9a^7+10b^9)(9a^7-10b^9)\\\\\\\frac{25}{36} a^4b^2-\frac{16}{49} c^6=\bigg(\frac{5}{6} a^2b\bigg)^2-\bigg(\frac{4}{7} c^3\bigg)^2=\\\\=\bigg(\frac{5}{6} a^2b-\frac{4}{7} c^3\bigg)\bigg(\frac{5}{6} a^2b+\frac{4}{7} c^3\bigg)$