упростите выражения(3ху+1)(3х+у)-у(3х+у)во 2 степени . Created by DASHA9996. algebra-ru

упростите выражения(3ху+1)(3х+у)-у(3х+у)во 2 степени ...

DASHA9996 @DASHA9996

July 2022 2 1 Report

упростите выражения
(3ху+1)(3х+у)-у(3х+у)во 2 степени

VandL

(3ху+1)(3х+у)-у(3х+у)^2=(3х+у)(3ху+1-3ху-у^2)=(3х+у)(1-у)(1+у)

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kefa

$(3xy+1)(3x+y)-y(3x+y)^2= \\ = 9x^2y+3xy^2+3x+y-y(9x^2+6xy+y^2)= \\ = \mathbf {9x^2y}+\mathit {3xy^2}+3x+y\mathbf{-9x^2y}\mathit{-6xy^2}-y^3= \\ = -3xy^2+3x+y-y^3= 3x(1-y^2)+y(1-y^2)= \\ = (3x+y)(1-y)(1+y)$

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