Упрости выражение (2а-3)^2-(3а-2)^2 и найди его значение при а= 9. Created by blomfield. matematika-ru

Упрости выражение (2а-3)^2-(3а-2)^2 и найди его значение при а= 9...

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July 2022 1 36 Report

Упрости выражение (2а-3)^2-(3а-2)^2 и найди его значение при а= 9

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NNNLLL54

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Ответ:

$a=9\\\\(2a-3)^2-(3a-2)^2=\\\\=\Big((2a-3)-(3a-2)\Big)\Big((2a-3)+(3a-2)\Big)=\\\\=(2a-3-3a+2)(2a-3+3a-2)=(-a-1)(5a-5)=\\\\=-5(a+1)(a-1)=-5(a^2-1)=-5\cdot (81-1)=5\cdot 80=400$

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