856. Представьте в виде произведения многочлен: 1) 3ab + 15b - 3а – 15; 2) 84-42y - 7xy + 14x; 3) abc + 6ac + 8ab + 48a; 4) m³ - m²n + m² mn; 5) a³ + a²-a-1; 6) 2x3 - 2xy² - 8x² + 8y²; 7) 5a² - 5b2 - 15a3b + 15ab³; 8) a²b² - 1-b² + a².

856.

• 1) 3ab + 15b - 3a - 15 = (3ab + 15b) + (-3a - 15) = 3b(a + 5) - 3(a + 5) = (3b - 3)(a + 5) = 3(b - 1)(a + 5)
• 2) 84 - 42y - 7xy + 14x = (84 - 42y) + (-7xy + 14x) = 42(2 - y) - 7x(y - 2) = 42(2 - y) + 7x(2 - y) = (42 + 7x)(2 - y) = 7(6 + x)(2 - y)
• 3) abc + 6ac + 8ab + 48a = (abc + 6ac) + (8ab + 48a) = ac(b + 6) + 8a(b + 6) = (ac + 8a)(b + 6) = a(c + 8)(b + 6)
• 4) m³ - m²n + m² - mn = (m³ - m²n) + (m² - mn) = m²(m - n) + m(m - n) = (m² + m)(m - n) = m(m + 1)(m - n)
• 5) a³ + a² - a - 1 = (a³ + a²) + (-a - 1) = a²(a + 1) - 1(a + 1) = (a² - 1)(a + 1) = (a - 1)(a + 1)(a + 1) = (a - 1)(a + 1)²
• 6) 2x³ - 2xy² - 8x² + 8y² = (2x³ - 2xy²) + (-8x² + 8y²) = 2x(x² - y²) - 8(x² - y²) = (2x - 8)(x² - y²) = 2(x - 4)(x - y)(x + y)
• 7) 5a² - 5b² - 15a³b + 15ab³ = (5a² - 5b²) + (-15a³b + 15ab³) = 5(a² - b²) - 15ab(a² - b²) = (5 - 15ab)(a² - b²) = 5(1 - 3ab)(a - b)(a + b)
• 8) a²b² - 1 - b² + a² = (a²b² - b²) + (a² - 1) = b²(a² - 1) + (a² - 1) = (b² + 1)(a² - 1) = (b² + 1)(a - 1)(a + 1)