1. Раскройте скобки. 1) (m + p)² 2) (u - v)² 3) (a + 4)² 4) (3 - c)² 5) (z + 9)² 6) (2x - h)² 7) (p + 2t)² 8) (12 - 6n)² 9) (5q + 14)² 10) (7k - 20)² 11) (2a + 3x)² 12) (10b - 9y)² 13) (17c + 3e)² 14) (6d - 19k)² 15) (15s + 2t)² 16) (m² - n)² 17) (5a² + 6b)² 18) (7b² - 3c²)² 19) (6y + x³p)² 20) (3n⁴l + 5n³)². Разложите на множители. 1) p² - 2pq + q² 2) u² + 2uv + v² 6) m² + 121v² - 22mv 7) 56bc + 16b² + 49c² 11) 400t² + 120bt + 9b² 12) 256u² - 416au + 169a²

1. Раскройте скобки.

1. \( (m + p)^2 = m^2 + 2mp + p^2 \)
2. \( (u - v)^2 = u^2 - 2uv + v^2 \)
3. \( (a + 4)^2 = a^2 + 2 \cdot 4 \cdot a + 4^2 = a^2 + 8a + 16 \)
4. \( (3 - c)^2 = 3^2 - 2 \cdot 3 \cdot c + c^2 = 9 - 6c + c^2 \)
5. \( (z + 9)^2 = z^2 + 2 \cdot 9 \cdot z + 9^2 = z^2 + 18z + 81 \)
6. \( (2x - h)^2 = (2x)^2 - 2 \cdot 2x \cdot h + h^2 = 4x^2 - 4xh + h^2 \)
7. \( (p + 2t)^2 = p^2 + 2 \cdot p \cdot 2t + (2t)^2 = p^2 + 4pt + 4t^2 \)
8. \( (12 - 6n)^2 = 12^2 - 2 \cdot 12 \cdot 6n + (6n)^2 = 144 - 144n + 36n^2 \)
9. \( (5q + 14)^2 = (5q)^2 + 2 \cdot 5q \cdot 14 + 14^2 = 25q^2 + 140q + 196 \)
10. \( (7k - 20)^2 = (7k)^2 - 2 \cdot 7k \cdot 20 + 20^2 = 49k^2 - 280k + 400 \)
11. \( (2a + 3x)^2 = (2a)^2 + 2 \cdot 2a \cdot 3x + (3x)^2 = 4a^2 + 12ax + 9x^2 \)
12. \( (10b - 9y)^2 = (10b)^2 - 2 \cdot 10b \cdot 9y + (9y)^2 = 100b^2 - 180by + 81y^2 \)
13. \( (17c + 3e)^2 = (17c)^2 + 2 \cdot 17c \cdot 3e + (3e)^2 = 289c^2 + 102ce + 9e^2 \)
14. \( (6d - 19k)^2 = (6d)^2 - 2 \cdot 6d \cdot 19k + (19k)^2 = 36d^2 - 228dk + 361k^2 \)
15. \( (15s + 2t)^2 = (15s)^2 + 2 \cdot 15s \cdot 2t + (2t)^2 = 225s^2 + 60st + 4t^2 \)
16. \( (m^2 - n)^2 = (m^2)^2 - 2 \cdot m^2 \cdot n + n^2 = m^4 - 2m^2n + n^2 \)
17. \( (5a^2 + 6b)^2 = (5a^2)^2 + 2 \cdot 5a^2 \cdot 6b + (6b)^2 = 25a^4 + 60a^2b + 36b^2 \)
18. \( (7b^2 - 3c^2)^2 = (7b^2)^2 - 2 \cdot 7b^2 \cdot 3c^2 + (3c^2)^2 = 49b^4 - 42b^2c^2 + 9c^4 \)
19. \( (6y + x^3p)^2 = (6y)^2 + 2 \cdot 6y \cdot x^3p + (x^3p)^2 = 36y^2 + 12x^3yp + x^6p^2 \)
20. \( (3n^4l + 5n^3)^2 = (3n^4l)^2 + 2 \cdot 3n^4l \cdot 5n^3 + (5n^3)^2 = 9n^8l^2 + 30n^7l + 25n^6 \)

2. Разложите на множители.

1. \( p^2 - 2pq + q^2 = (p - q)^2 \)
2. \( u^2 + 2uv + v^2 = (u + v)^2 \)
3. \( m^2 + 121v^2 - 22mv = m^2 - 22mv + 121v^2 = (m - 11v)^2 \)
4. \( 56bc + 16b^2 + 49c^2 = 16b^2 + 56bc + 49c^2 = (4b + 7c)^2 \)
5. \( 400t^2 + 120bt + 9b^2 = (20t + 3b)^2 \)
6. \( 256u^2 - 416au + 169a^2 = (16u - 13a)^2 \)