Номер 1.

1. (5m + 4n)(4n - 5m) = (4n + 5m)(4n - 5m) = 16n² - 25m²

2. (9a² - 1/2m³c)(9a² + 1/2m³c) = 81a⁴ - 1/4m⁶c²

3. (7x - 3y)² = (7x)² - 2 × 7x × 3y + (3y)² = 49x² - 42xy + 9y²

4. (1,25a² + 8b)² = (1,25a²)² + 2 × 1,25a² × 8b + (8b)² = 1,5625a⁴ + 20a²b + 64b²

Номер 2.

1. 36a² - 49b² = (6a - 7b)(6a + 7b)

2. x² - 8xy + 16y² = x² - 2 × x × 4y + (4y)² = (x - 4y)²

Номер 3.

1. 1000 - m³ = (10 - m)(10² + 10 × m + m²) = (10 - m)(100 + 10m + m²)

2. 1/8 + 8c⁶ = 1/8(1 + 64c⁶) = 1/8(1 + 4c²)(1 - 4c² + 16c⁴)

Номер 4.

1. 5a⁵b³ - 40a²b⁶ = 5a²b³(1 - 8b³) = 5a²b³(1 - 2b)(1 + 2b + 4b²)

2. a² - b² + a + b = (a² - b²) + (a + b) = (a - b)(a + b) + a + b = (a + b)(a - b + 1)

Номер 5.

1. (x + 2)² - 9x² = 0

x² + 4x + 4 - 9x² = 0

- 8x² + 4x + 4 = 0 | ÷ - 4

2x² - x - 1 = 0

a = 2, b = - 1, c = - 1

D = b² - 4ac = (- 1)² - 4 × 2 × (- 1) = 1 + 8 = 9 = 3²

x1 = (1 - 3)/4 = - 2/4 = - 1/2

x2 = (1 + 3)/4 = 4/4 = 1

Ответ : x1 = - 1/2, x2 = 1

2. 25у² + 10у + 1 = 0

а = 25, b = 10, c = 1

D = 10² - 4 × 25 × 1 = 100 - 100 = 0

x = - b/2a = - 10/50 = - 1/5

Ответ : х = - 1/5