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Anntyan28
@Anntyan28
July 2022
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tan4ik3107
А) 1-4х²+8ху-4у²=
1-4(х²-2ху+у²)=
1-4(х-у)²=
(1-2(х-у))(1+2(х-у))
б) 125в³-5в²+в-1=
(5³в³-1)-в(5в-1)=
(5в-1)(25в²-5в+1)-в(5в-1)=
(5в-1)(25в²-5в+1-в)=
(5в-1)(25в²-6в+1)
в) (у²+2)²-(6у+7)²=
(у²+2-(6у+7))(у²+2+6у+7)=
(у²+2-6у-7)(у²+2+6у+7)=
(у²-6у-5)(у²+6у+9)=
(у²-6у-5)(у+3)²=
(у²-6у-5)(у+3)(у+3)
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Answers & Comments
1-4(х²-2ху+у²)=
1-4(х-у)²=
(1-2(х-у))(1+2(х-у))
б) 125в³-5в²+в-1=
(5³в³-1)-в(5в-1)=
(5в-1)(25в²-5в+1)-в(5в-1)=
(5в-1)(25в²-5в+1-в)=
(5в-1)(25в²-6в+1)
в) (у²+2)²-(6у+7)²=
(у²+2-(6у+7))(у²+2+6у+7)=
(у²+2-6у-7)(у²+2+6у+7)=
(у²-6у-5)(у²+6у+9)=
(у²-6у-5)(у+3)²=
(у²-6у-5)(у+3)(у+3)