Разложите на множители: x⁴+y⁴+2x³y+2x²y²+2xy³ С объяснениями.. Created by madinashaizaman. algebra-ru

Разложите на множители: x⁴+y⁴+2x³y+2x²y²+2xy³ С объяснениями...

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julyap $x^{4} +y^{4} +2 x^{2} y+2 x^{2} y ^{2} +2xy ^{3} = x^{4} +y ^{4} +2 x^{2} y ^{2} +2 x^{3} y+3xy ^{3} = \\ =( x^{2} +y ^{2} ) ^{2} +2xy( x^{2} +y ^{2} )=( x^{2} +y ^{2} )( x^{2} +y ^{2} +2xy)= \\ =( x^{2} +y ^{2} )(x+y) ^{2}$

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