Question

(8x-4y)²(10x+5y)²(-3-4)²(2a-1)³​

Answer 1

Пояснение:

Воспользуемся формулами сокращённого умножения.

Квадрат суммы:

(a + b)² = (a + b) (a + b) =

= a² + ab + ab + b² =

= a² + 2ab + b².

Квадрат разности:

(a - b)² = (a - b) (a - b) =

= a² - ab - ab + b² =

= a² - 2ab + b².

Куб разности:

(a - b)³ =

= a³ - 3a²b + 3ab² - b³.

Решение/ответ:

1) (8x - 4y)² =

= (8x)² - (2 × 8x × 4y) + (4y)² =

= 64x² - 64xy + 16y².

2) (10x + 5y)² =

= (10x)² + (2 × 10x × 5y) + (5y)² =

= 100x² + 100xy + 25y².

3) (- 3 - 4)² =

= (- 3)² - (2 × (- 3) × 4) + 4² =

= 9 - (- 24) + 16 =

(при раскрытии скобок: если перед скобками стоит "-", то знаки внутри скобок меняем на противоположные)

= 9 + 24 + 16 =

= 49.

4) (2a - 1)³ =

= (2a)³ - (3 × (2a)² × 1) + (3 × 2a × 1²) - 1³ =

= (2a)³ - (3 × 4a² × 1) + (3 × 2a × 1²) - 1³ =

= 8a³ - 12a² + 6a - 1³ =

= 8a³ - 12a² + 6a - 1.

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Answer 2

Ответ:

(8x-4y)²=64x²-64xy+16y²

(10x+5y)²=100x²+100xy+25y²

(-3-4)²=(-7)²=49

(2a-1)³=8a³-12a²+6a-1

Объяснение:

Answer 3

To simplify the given expression, let's break it down step by step:

(8x - 4y)² = (8x - 4y)(8x - 4y) = 64x² - 32xy - 32xy + 16y² = 64x² - 64xy + 16y²

(10x + 5y)² = (10x + 5y)(10x + 5y) = 100x² + 50xy + 50xy + 25y² = 100x² + 100xy + 25y²

(-3 - 4)² = (-7)² = 49

(2a - 1)³ = (2a - 1)(2a - 1)(2a - 1) = (4a² - 2a - 2a + 1)(2a - 1) = (4a² - 4a + 1)(2a - 1) = 8a³ - 4a² - 8a² + 4a + 2a - 1 = 8a³ - 12a² + 6a - 1

Now, let's combine all the simplified terms:

(64x² - 64xy + 16y²)(100x² + 100xy + 25y²)(49)(8a³ - 12a² + 6a - 1)

Multiplying all these terms together would result in a very lengthy expression, which may not be practical to write out in this format. However, the above expression represents the simplified form of the given expression.