Представьте в виде произведения многочлен:
1) 3ab + 15b − 3a − 15;
2) 84 − 42y − 7xy + 14x;
3) abc + 6ac + 8ab + 48a;
4)

m^{3} - m^{2} n + m^{2} - m n

;
5)

a^{3} + a^{2} - a - 1

;
6)

2 x^{3} - 2 x y^{2} - 8 x^{2} + 8 y^{2}

;
7)

5 a^{2} - 5 b^{2} - 15 a^{3} b + 15 a b^{3}

;
8)

a^{2} b^{2} - 1 - b^{2} + a^{2}

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Алгебре 7 класс Мерзляк. Номер №717

3ab + 15b − 3a − 15 = (3ab + 15b) − (3a + 15) = 3b(a + 5) − 3(a + 5) = (a + 5)(3b − 3) = 3(a + 5)(b − 1)

84 − 42y − 7xy + 14x = (84 − 42y) − (7xy − 14x) = 42(2 − y) − 7x(y − 2) = (2 − y)(42 + 7x) = 7(2 − y)(6 + x)

abc + 6ac + 8ab + 48a = (abc + 6ac) + (8ab + 48a) = ac(b + 6) + 8a(b + 6) = (b + 6)(ac
+ 8a) = a(b + 6)(c + 8)

m^{3} - m^{2} n + m^{2} - m n = (m^{3} - m^{2} n) + (m^{2} - m n) = m^{2} (m - n) + m (m - n) = (m - n) (m^{2} + m) = m (m - n) (m + 1)

a^{3} + a^{2} - a - 1 = (a^{3} + a^{2}) - (a + 1) = a^{2} (a + 1) - (a + 1) = (a + 1) (a^{2} - 1) = (a + 1) (a - 1) (a + 1)

2 x^{3} - 2 x y^{2} - 8 x^{2} + 8 y^{2} = (2 x^{3} - 2 x y^{2}) - (8 x^{2} - 8 y^{2}) = 2 x (x^{2} - y^{2}) - 8 (x^{2} - y^{2}) = (x^{2} - y^{2}) (2 x - 8) = 2 (x^{2} - y^{2}) (x - 4) = 2 (x - y) (x + y) (x - 4)

5 a^{2} - 5 b^{2} - 15 a^{3} b + 15 a b^{3} = (5 a^{2} - 5 b^{2}) - (15 a^{3} b - 15 a b^{3}) = 5 (a^{2} - b^{2}) - 15 a b (a^{2} - b^{2}) = (a^{2} - b^{2}) (5 - 15 a b) = 5 (a^{2} - b^{2}) (1 - 3 a b) = 5 (a - b) (a + b) (1 - 3 a b)

a^{2} b^{2} - 1 - b^{2} + a^{2} = (a^{2} b^{2} + a^{2}) - (1 + b^{2}) = a^{2} (b^{2} + 1) - (b^{2} + 1) = (b^{2} + 1) (a^{2} - 1) = (b^{2} + 1) (a - 1) (a + 1)

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир