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Разложите многочлен на множители:
1)(х+у)³-(х-у)³-2у
2)х³-27+(х+3)²-3х
Разложите многочлен на множители:
1)(х+у)³-(х-у)³-2у
2)х³-27+(х+3)²-3х
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Answers & Comments
Verified answer
(х+у)³-(х-у)³-2у=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y=6x^2y+2y^3-2y=2y(3x^2+y^2-1)
х³-27+(х+3)²-3х==x^3-27+x^2+6x+9-3x=x^3+x^2+3x-18=
x^2(x-2)+3x(x-2)+9(x-2)=(x-2)(x^2+3x+9)
Verified answer
1)(х+у)³-(х-у)³-2у= x³+3x²y+3xy²+y³-(x³-3x²y+3xy²-y³)-2y = x³-x³+3x²y +3x²y +3xy² -3xy² +y³+y³ -2y= 6x²y+2y³-2y=2y(3x²+y²-1)2)х³-27+(х+3)²-3х = (x-3)(x²+3x+9)+x²+6x+9-3x = (x-3+1)(x²+3x+9)=(x-2)(x²+3x+9)