Предмет: Алгебра, автор: letusik48

Упростить выражения:
1) (2x+y)²-(2z-y)2-4x(y+2)=...
2) (x+2y)³-x(6xy+9x²+18y²)-7y³=...
3) (x-3)²+(x-3)³-(x-3)(x²-3)=...​

Ответы

Автор ответа: Аноним
1

Объяснение:

1) (2х+у)²-(2z-y)2-4x(y+2) - раскроем скобки по формуле сокращенного умножения:

4х²+4ху+у²-(4z-2y)-4xy-8x - сократим противоположные выражения ±4ху и раскроем отрицательную скобку с противоположным знаком:

4х²+у²-4z+2y-8x (ответ)

2) (х+2у)³-х(6ху+9х²+18у²)-7у³ - раскроем скобки по формуле сокращенного умножения:

х³+6х²у+12ху²+8у³-6х²у-9х³-18ху²-7у³ - скоращаем проивоположные выражения (±6х²у и т.п.):

-8х³-6ху²+у³ (ответ)

3) (х-3)²+(х-3)³-(х-3)(х²-3) - выносим за скобки общий множитель х-3:

(х-3)×(х-3+(х-3)²-(х²-3)) - разложим выражения во второй скобке на более мелкие для простоты решения примера:

(х-3)×(х-3+(х-3)²-х²+3) - сократим противоположные выражения (например ±3 и т.п.):

(х-3)×(х+х²-6х+9-х²) - сокращаем проивоположные ±х и -6 и 9 на 3:

(х-3)(-5х+9) - ответ

letusik48: Огромное спасибо, очень очень помогли!!!!
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