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PlotnikovaMari
@PlotnikovaMari
August 2022
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разложить многочлен на множители
(x +y)³ - (x -y)³-2у
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oganesbagoyan
Verified answer
разложить многочлен на множители (x +y)³ - (x -y)³-2у
-----
(x + y)³ - (x - y)³- 2y = x³ +3x²y +3xy² +y³ - (
x³ - 3x²y +3xy² - y³ ) -2y =
x³ +
3x²y
+3xy² +y³ -
x³ +
3x²y
-3xy² + y³ -2y =
6x²y +2y³ -2y = 2y(3x² +y² -1).
--- ил
и по формуле разности кубов: (a
³ - b³ =(a - b)(a² +ab+b²) .
(x
+ y)³ - (x -y)³ - 2y =(
(x
+ y )- (x -y)) ( (x + y )² + (x + y )(x - y) +(x - y)² )² -
2y =
2y(x² +2xy +y² + x² - y² +x² -2xy +y²) -2y =2y(3x² +y² -1).
2 votes
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Verified answer
разложить многочлен на множители (x +y)³ - (x -y)³-2у-----
(x + y)³ - (x - y)³- 2y = x³ +3x²y +3xy² +y³ - ( x³ - 3x²y +3xy² - y³ ) -2y =
x³ +3x²y +3xy² +y³ - x³ + 3x²y -3xy² + y³ -2y = 6x²y +2y³ -2y = 2y(3x² +y² -1).
--- или по формуле разности кубов: (a³ - b³ =(a - b)(a² +ab+b²) .
(x + y)³ - (x -y)³ - 2y =( (x + y )- (x -y)) ( (x + y )² + (x + y )(x - y) +(x - y)² )² - 2y =
2y(x² +2xy +y² + x² - y² +x² -2xy +y²) -2y =2y(3x² +y² -1).