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mnbnata
@mnbnata
July 2022
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докажите что значение выражения (2а+3b) в квадрате + (2а -3b) в квадрате - 2 ( 2а+3b)( 3b-2a) - (8a-5)(2a+3) + 2(7a-15) не зависит от значений переменных
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Pacanka202
(2а+3b)^2+(2a–3b)^2–2(2a+3b)(3b–2a)–(8a–5)(2a+3)+2(7a–15) =
= 4a^2+12ab+9b^2+4a^2–12ab+9b^2+2(2a+3b)(2a–3b)–(16a^2+24a–10a–15)+14a–30 =
= 8a^2+18b^2+2(4a^2–9b^2)–16a^2–14a+15+14a–30 =
=8a^2+18b^2+8a^2–18b^2–16a^2–15 = –15
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Answers & Comments
= 4a^2+12ab+9b^2+4a^2–12ab+9b^2+2(2a+3b)(2a–3b)–(16a^2+24a–10a–15)+14a–30 =
= 8a^2+18b^2+2(4a^2–9b^2)–16a^2–14a+15+14a–30 =
=8a^2+18b^2+8a^2–18b^2–16a^2–15 = –15