Задание 5. Разложите на множители: 1. (5x + 2)(x - 6) 2. (3x - 4)(4x + 3) 3. (6x + 1)(2x - 5) 4. (x - 8)(7x + 2) 5. (4x - 3)(5x + 4) 6. (2x + 9)(x - 7)

Задание 5

1. \( (5x + 2)(x - 6) = 5x · x + 5x · (-6) + 2 · x + 2 · (-6) = 5x^2 - 30x + 2x - 12 = 5x^2 - 28x - 12 \)
2. \( (3x - 4)(4x + 3) = 3x · 4x + 3x · 3 - 4 · 4x - 4 · 3 = 12x^2 + 9x - 16x - 12 = 12x^2 - 7x - 12 \)
3. \( (6x + 1)(2x - 5) = 6x · 2x + 6x · (-5) + 1 · 2x + 1 · (-5) = 12x^2 - 30x + 2x - 5 = 12x^2 - 28x - 5 \)
4. \( (x - 8)(7x + 2) = x · 7x + x · 2 - 8 · 7x - 8 · 2 = 7x^2 + 2x - 56x - 16 = 7x^2 - 54x - 16 \)
5. \( (4x - 3)(5x + 4) = 4x · 5x + 4x · 4 - 3 · 5x - 3 · 4 = 20x^2 + 16x - 15x - 12 = 20x^2 + x - 12 \)
6. \( (2x + 9)(x - 7) = 2x · x + 2x · (-7) + 9 · x + 9 · (-7) = 2x^2 - 14x + 9x - 63 = 2x^2 - 5x - 63 \)

Ответ: 1. 5x² - 28x - 12; 2. 12x² - 7x - 12; 3. 12x² - 28x - 5; 4. 7x² - 54x - 16; 5. 20x² + x - 12; 6. 2x² - 5x - 63.