Expand the following expressions using the formula (a+b)² = a² + 2ab + b²:

Решение:

Используем формулу квадрата суммы: \( (a+b)^2 = a^2 + 2ab + b^2 \).

1. \( (x+1)^2 = x^2 + 2 \cdot x \cdot 1 + 1^2 = x^2 + 2x + 1 \)
2. \( (a-3)^2 = a^2 - 2 \cdot a \cdot 3 + 3^2 = a^2 - 6a + 9 \)
3. \( (y+3)^2 = y^2 + 2 \cdot y \cdot 3 + 3^2 = y^2 + 6y + 9 \)
4. \( (B-4)^2 = B^2 - 2 \cdot B \cdot 4 + 4^2 = B^2 - 8B + 16 \)
5. \( (c+5)^2 = c^2 + 2 \cdot c \cdot 5 + 5^2 = c^2 + 10c + 25 \)
6. \( (6-d)^2 = 6^2 - 2 \cdot 6 \cdot d + d^2 = 36 - 12d + d^2 \)
7. \( (7+g)^2 = 7^2 + 2 \cdot 7 \cdot g + g^2 = 49 + 14g + g^2 \)
8. \( (8-h)^2 = 8^2 - 2 \cdot 8 \cdot h + h^2 = 64 - 16h + h^2 \)
9. \( (9+k)^2 = 9^2 + 2 \cdot 9 \cdot k + k^2 = 81 + 18k + k^2 \)
10. \( (10-m)^2 = 10^2 - 2 \cdot 10 \cdot m + m^2 = 100 - 20m + m^2 \)
11. \( (n+11)^2 = n^2 + 2 \cdot n \cdot 11 + 11^2 = n^2 + 22n + 121 \)
12. \( (p-12)^2 = p^2 - 2 \cdot p \cdot 12 + 12^2 = p^2 - 24p + 144 \)
13. \( (q+13)^2 = q^2 + 2 \cdot q \cdot 13 + 13^2 = q^2 + 26q + 169 \)
14. \( (r-14)^2 = r^2 - 2 \cdot r \cdot 14 + 14^2 = r^2 - 28r + 196 \)
15. \( (s+15)^2 = s^2 + 2 \cdot s \cdot 15 + 15^2 = s^2 + 30s + 225 \)