ГДЗ до підручника «Алгебра» H.А. Тарасенкової. 7 клас

671.6y12 - 27 = 232)3(y4)3 - 33 = (2х2y4 - 3)(4x4y8 + 6х2у4 + 9). Вираз 3).

673. 27a3 - 0,001c3 = (3a - 0,1c)(9a2 + 0,3ac + 0,01c2).

676. 1) (a3 + b3)(a3 - b3) = a6 - b6;

2) (27x3 - y3)(27x3 + y3) = 729x6 - y6;

3) (m3 - 0,0001n3)(m3 + 0,001n3) = (m3)2 - (0,01n3)2 = m6 - 0,000001n6.

677. 1) (64c3 + b3)(64c3 - b3) = (4096c6 - b6;

2) (a3 + 0,125t3)(a3 - 0,125t3) = n6 - 0,015625t6.

678. 1) (1 + x3)(1 - x3) = 1 - x6 = 1 - 26 = 1 - 64 = -63;

2) (8a3 - 125b3) - 8a3 = 8a3 - 125b3 - 8a3 = -125b3 = -125 • (-0,1)3 = -125 • (-0,001) = 0,125;

679. 1) (3 + b)3 - b3 = ((3 + b) - b)((3 + b)2 + b • (3 + b) + b2) = 3 • (9 + 6b + b2 + 3b + b2 + b2) = 3 • (3b2 + 9b + 9) = 9(b2 + 3b + 3) = 9b2 + 27b + 27;

2) (5 - 4a)3 + 64a3 = (5 - 4a + 4a)((5 - 4a)2 - 4a(5 - 4a) + (4a)2) = 5 • (25 - 40a + 16a2 - 20a + 16a2 + 16a2) = 5(48a2 - 60a + 25) = 240a2 - 300a + 125;

3) 343y6 - (5 + 7y2)3 = (7y2 - (5 + 7y2)) • ((7y2)2 + 7y2(5 + 7y2) + (5 + 7y2)2) = -5(49y4 + 35y2 + 49y4 + 25 + 70y2 + 49y4) = -5(147y4 + 105y2 + 25 = -735y4 - 525y2 - 125;

4) 125x3 - (5x + 1)3 = (5x - (5x + 1))((5x)2 + 5x(5x + 1) + (5x + 1)2) = -1 • (25x2 + 25x2 + 5x + 25x2 + 10x + 1) = -1 • (75x2 + 15x + 1) = -75x2 - 15x - 1.


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