570. Выполните возведение в квадрат: 1) (a + 8)²; 2) (b-2)2; 3) (7 + c)²; 4) (6-d); 2 5) (2m + 1)²; 2 2 6) (4x-3); 7) (5m - 4n)2; 8) (10c + 7d)²; 1 2 2 Y; 9) (4x-y 10) (0,3a +0,9b)²; 571. Упростите выражение: 1) a² + (3a - b)2; 2) (4x + 5)240x; 3) 50a²(7a- 1)2; 4) с² +36 (с – 6)2; 5) (x-2)² + x(x + 10); 572. Упростите выражение: 1) (x – 12)² + 24x; 2) (x + 8)2 x(x + 5); 3) 2x(x + 2) - (x - 2)2;

570. Выполните возведение в квадрат:

1. \[(a + 8)^2 = a^2 + 2 \cdot a \cdot 8 + 8^2 = a^2 + 16a + 64\]
2. \[(b - 2)^2 = b^2 - 2 \cdot b \cdot 2 + 2^2 = b^2 - 4b + 4\]
3. \[(7 + c)^2 = 7^2 + 2 \cdot 7 \cdot c + c^2 = 49 + 14c + c^2\]
4. \[(6 - d)^2 = 6^2 - 2 \cdot 6 \cdot d + d^2 = 36 - 12d + d^2\]
5. \[(2m + 1)^2 = (2m)^2 + 2 \cdot 2m \cdot 1 + 1^2 = 4m^2 + 4m + 1\]
6. \[(4x - 3)^2 = (4x)^2 - 2 \cdot 4x \cdot 3 + 3^2 = 16x^2 - 24x + 9\]
7. \[(5m - 4n)^2 = (5m)^2 - 2 \cdot 5m \cdot 4n + (4n)^2 = 25m^2 - 40mn + 16n^2\]
8. \[(10c + 7d)^2 = (10c)^2 + 2 \cdot 10c \cdot 7d + (7d)^2 = 100c^2 + 140cd + 49d^2\]
9. \[\left(4x - \frac{1}{8}y\right)^2 = (4x)^2 - 2 \cdot 4x \cdot \frac{1}{8}y + \left(\frac{1}{8}y\right)^2 = 16x^2 - xy + \frac{1}{64}y^2\]
10. \[(0.3a + 0.9b)^2 = (0.3a)^2 + 2 \cdot 0.3a \cdot 0.9b + (0.9b)^2 = 0.09a^2 + 0.54ab + 0.81b^2\]
11. \[(c^2 - 6)^2 = (c^2)^2 - 2 \cdot c^2 \cdot 6 + 6^2 = c^4 - 12c^2 + 36\]
12. \[(15 + k^2)^2 = 15^2 + 2 \cdot 15 \cdot k^2 + (k^2)^2 = 225 + 30k^2 + k^4\]
13. \[(m^2 - 3n)^2 = (m^2)^2 - 2 \cdot m^2 \cdot 3n + (3n)^2 = m^4 - 6m^2n + 9n^2\]
14. \[(m^4 - n^3)^2 = (m^4)^2 - 2 \cdot m^4 \cdot n^3 + (n^3)^2 = m^8 - 2m^4n^3 + n^6\]
15. \[(5a^4 - 2a^7)^2 = (5a^4)^2 - 2 \cdot 5a^4 \cdot 2a^7 + (2a^7)^2 = 25a^8 - 20a^{11} + 4a^{14}\]

571. Упростите выражение:

1. \[a^2 + (3a - b)^2 = a^2 + (9a^2 - 6ab + b^2) = a^2 + 9a^2 - 6ab + b^2 = 10a^2 - 6ab + b^2\]
2. \[(4x + 5)^2 - 40x = (16x^2 + 40x + 25) - 40x = 16x^2 + 40x + 25 - 40x = 16x^2 + 25\]
3. \[50a^2 - (7a - 1)^2 = 50a^2 - (49a^2 - 14a + 1) = 50a^2 - 49a^2 + 14a - 1 = a^2 + 14a - 1\]
4. \[c^2 + 36 - (c - 6)^2 = c^2 + 36 - (c^2 - 12c + 36) = c^2 + 36 - c^2 + 12c - 36 = 12c\]
5. \[(x - 2)^2 + x(x + 10) = (x^2 - 4x + 4) + (x^2 + 10x) = x^2 - 4x + 4 + x^2 + 10x = 2x^2 + 6x + 4\]
6. \[3m(m - 4) - (m + 2)^2 = 3m^2 - 12m - (m^2 + 4m + 4) = 3m^2 - 12m - m^2 - 4m - 4 = 2m^2 - 16m - 4\]
7. \[(y - 9)^2 + (4 - y)(y + 6) = (y^2 - 18y + 81) + (4y + 24 - y^2 - 6y) = y^2 - 18y + 81 + 4y + 24 - y^2 - 6y = -20y + 105\]
8. \[(x - 4)(x + 4) - (x - 1)^2 = (x^2 - 16) - (x^2 - 2x + 1) = x^2 - 16 - x^2 + 2x - 1 = 2x - 17\]
9. \[(2a - 3b)^2 + (3a + 2b)^2 = (4a^2 - 12ab + 9b^2) + (9a^2 + 12ab + 4b^2) = 4a^2 - 12ab + 9b^2 + 9a^2 + 12ab + 4b^2 = 13a^2 + 13b^2\]
10. \[(x - 5)^2 - (x - 7)(x + 7) = (x^2 - 10x + 25) - (x^2 - 49) = x^2 - 10x + 25 - x^2 + 49 = -10x + 74\]

572. Упростите выражение:

1. \[(x - 12)^2 + 24x = x^2 - 24x + 144 + 24x = x^2 + 144\]
2. \[(x + 8)^2 - x(x + 5) = x^2 + 16x + 64 - x^2 - 5x = 11x + 64\]
3. \[2x(x + 2) - (x - 2)^2 = 2x^2 + 4x - (x^2 - 4x + 4) = 2x^2 + 4x - x^2 + 4x - 4 = x^2 + 8x - 4\]
4. \[(y + 7)^2 + (y + 2)(y - 7) = y^2 + 14y + 49 + y^2 - 7y + 2y - 14 = 2y^2 + 9y + 35\]
5. \[(a + 1)(a - 1) - (a + 4)^2 = a^2 - 1 - (a^2 + 8a + 16) = a^2 - 1 - a^2 - 8a - 16 = -8a - 17\]
6. \[(x - 10)(9 - x) + (x + 10)^2 = 9x - x^2 - 90 + 10x + x^2 + 20x + 100 = 39x + 10\]

Ответ: См. подробное решение выше