3. Разложите на множители: 1) a) 2a + b + 2a² + ab; 6) 3a + 3a² - b - ab; 2) a) ab + ac + am + yb + yc + ym; 6) xy - x²y² + xy² - a + axy - ax²y²; 3) a) bⁿ⁺¹ + bⁿ+b+1; 6) aⁿ⁺²-1-a+aⁿ⁺¹.

Ответ:

1. a) \(2a + b + 2a^2 + ab = (2a + 2a^2) + (b + ab) = 2a(1 + a) + b(1 + a) = (1 + a)(2a + b)\)
2. б) \(3a + 3a^2 - b - ab = (3a + 3a^2) + (-b - ab) = 3a(1 + a) - b(1 + a) = (1 + a)(3a - b)\)
3. a) \(ab + ac + am + yb + yc + ym = (ab + ac + am) + (yb + yc + ym) = a(b + c + m) + y(b + c + m) = (b + c + m)(a + y)\)
4. б) \(xy - x^2y^2 + xy^2 - a + axy - ax^2y = (xy - x^2y^2 + xy^2) + (-a + axy - ax^2y) = xy(1 - xy + y) - a(1 - xy + y) = (1 - xy + y)(xy - a)\)
5. a) \(b^{n+1} + b^n + b + 1 = (b^{n+1} + b^n) + (b + 1) = b^n(b + 1) + (b + 1) = (b + 1)(b^n + 1)\)
6. б) \(a^{n+2} - 1 - a + a^{n+1} = (a^{n+2} + a^{n+1}) + (-a - 1) = a^{n+1}(a + 1) - (a + 1) = (a + 1)(a^{n+1} - 1)\)

Ответ: