Контрольная алгебра 7 класс Звавич, Кузнецова

Вариант 1

к-7

 

1. a) (y - 4)2 = y2 - 8y + 16;
б) (7х + a)2 = 49x2 + 14ax + a2;
в) (5c - 1)(5c + 1) = 25c2 - 1;
г) (3а + 2b)(3a - 2b) = 9a2 - 4b2.

2. (a - 9)2 - (81 + 2a) = a2 - 18a + 81 - 81 - 2a = a2 - 20a.

3. а) x2 - 49 = (x - 7)(х + 7);
б) 25x2 - 10xy + y2 = (5x - y)2 = (5x - y)(5x - y).

4. (2 - x)2 - x(x + 1,5) = 4;
4 - 4x + x2 - x2 - 1,5x = 4;
5,5x = 0;
x = 0.

5. a) (y2 - 2a)(2a + y2) = y4 - 4a2;
6) (3x2 + x)2 = 9x4 + 6x3 + x2;
в) (2 + m)2(2 - m)2 = ((2 + m)(2 - m))2 = (4 - m2)2 = 16 - 8m2 + m4.

6. а) 4x2y2 - 9a4 = (2xy - 3a2)(2xy + 3a2);
б) 25a2 - (a + 3)2 = (5a - a - 3)(5a + a + 3) = (4a - 3)(6a + 3) = 3(2a + 1)(4a - 3);
в) 27m3 + n3 = (3m + n)(9m2 - 3mn + n2).