Выполните умножение:
1) (x + 2)(x − 1)(x − 4);
2) (2x + 1)(x + 5)(x − 6);
3)

(x^{2} - 2 x + 3) (x^{2} + 2 x - 3)

;
4) (a + 2b − c)(a − 3b + 2c);
5)

(a + b) (a^{3} - a^{2} b + a b^{2} - b^{3})

;
6)

(x - 1) (x^{4} + x^{3} + x^{2} + x + 1)

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Алгебре 7 класс Мерзляк. Номер №400

(x + 2) (x - 1) (x - 4) = (x^{2} + 2 x - x - 2) (x - 4) = x^{3} + 2 x^{2} - x^{2} - 2 x - 4 x^{2} - 8 x + 4 x + 8 = x^{3} + (2 x^{2} - x^{2} - 4 x^{2}) + (- 2 x - 8 x + 4 x) + 8 = x^{3} - 3 x^{2} - 6 x + 8

(2 x + 1) (x + 5) (x - 6) = (2 x^{2} + x + 10 x + 5) (x - 6) = 2 x^{3} + x^{2} + 10 x^{2} + 5 x - 12 x^{2} - 6 x - 60 x - 30 = 2 x^{3} + (x^{2} + 10 x^{2} - 12 x^{2}) + (5 x - 6 x - 60 x) - 30 = 2 x^{3} - x^{2} - 61 x

(x^{2} - 2 x + 3) (x^{2} + 2 x - 3) = x^{4} - 2 x^{3} + 3 x^{2} + 2 x^{3} - 4 x^{2} + 6 x - 3 x^{2} + 6 x - 9 = x^{4} - (- 2 x^{3} + 2 x^{3}) + (3 x^{2} - 4 x^{2} - 3 x^{2}) + (6 x + 6 x) - 9 = x^{4} - 4 x^{2} + 12 x - 9

(a + 2 b - c) (a - 3 b + 2 c) = a^{2} - 3 a b + 2 a c + 2 a b - 6 b^{2} + 4 b c - a c + 3 b c - 2 c^{2} = a^{2} + (- 3 a b + 2 a b) + (2 a c - a c) + (4 b c + 3 b c) - 6 b^{2} - 2 c^{2} = a^{2} - a b + a c + 7 b c - 6 b^{2} - 2 c^{2}

(a + b) (a^{3} - a^{2} b + a b^{2} - b^{3}) = a^{4} - a^{3} b + a^{2} b^{2} - a b^{3} + a^{3} b - a^{2} b^{2} + a b^{3} - b^{4} = a^{4} + (- a^{3} b + a^{3} b) + (a^{2} b^{2} - a^{2} b^{2}) + (- a b^{3} + a b^{3}) - b^{4} = a^{4} + 0 + 0 + 0 - b^{4} = a^{4} - b^{4}

(x - 1) (x^{4} + x^{3} + x^{2} + x + 1) = x^{5} + x^{4} + x^{3} + x^{2} + x - x^{4} - x^{3} - x^{2} - x - 1 = x^{5} + (x^{4} - x^{4}) + (x^{3} - x^{3}) + (x^{2} - x^{2}) + (x - x) - 1 = x^{5} + 0 + 0 + 0 + 0 - 1 = x^{5} - 1

ГДЗ Алгебра 7 класс Мерзляк, Полонский, Якир