(m^2 + 2)^2

Для решения этих примеров воспользуемся формулами сокращенного умножения: $(a + b)^2 = a^2 + 2ab + b^2$ $(a - b)^2 = a^2 - 2ab + b^2$ 1. $(m^2 + 2)^2 = (m^2)^2 + 2 \cdot m^2 \cdot 2 + 2^2 = m^4 + 4m^2 + 4$ 2. $(n^2 - 3)^2 = (n^2)^2 - 2 \cdot n^2 \cdot 3 + 3^2 = n^4 - 6n^2 + 9$ 3. $(2x + y^2)^2 = (2x)^2 + 2 \cdot 2x \cdot y^2 + (y^2)^2 = 4x^2 + 4xy^2 + y^4$ 4. $(3p - k^2)^2 = (3p)^2 - 2 \cdot 3p \cdot k^2 + (k^2)^2 = 9p^2 - 6pk^2 + k^4$ 5. $(4p^2 + k^2)^2 = (4p^2)^2 + 2 \cdot 4p^2 \cdot k^2 + (k^2)^2 = 16p^4 + 8p^2k^2 + k^4$ 6. $(8x^2 - 0,2)^2 = (8x^2)^2 - 2 \cdot 8x^2 \cdot 0,2 + 0,2^2 = 64x^4 - 3,2x^2 + 0,04$ 7. $(\frac{5}{6}x^2 + 3)^2 = (\frac{5}{6}x^2)^2 + 2 \cdot \frac{5}{6}x^2 \cdot 3 + 3^2 = \frac{25}{36}x^4 + 5x^2 + 9$ 8. $(\frac{1}{8}x^2 - 4n)^2 = (\frac{1}{8}x^2)^2 - 2 \cdot \frac{1}{8}x^2 \cdot 4n + (4n)^2 = \frac{1}{64}x^4 - x^2n + 16n^2$ 9. $(\frac{2}{7}m + 7n^3)^2 = (\frac{2}{7}m)^2 + 2 \cdot \frac{2}{7}m \cdot 7n^3 + (7n^3)^2 = \frac{4}{49}m^2 + 4mn^3 + 49n^6$ 10. $(\frac{1}{6}p^3 + 3n)^2 = (\frac{1}{6}p^3)^2 + 2 \cdot \frac{1}{6}p^3 \cdot 3n + (3n)^2 = \frac{1}{36}p^6 + p^3n + 9n^2$ 11. $(\frac{3}{5}c^3 + 5t^4)^2 = (\frac{3}{5}c^3)^2 + 2 \cdot \frac{3}{5}c^3 \cdot 5t^4 + (5t^4)^2 = \frac{9}{25}c^6 + 6c^3t^4 + 25t^8$ 12. $(x^2y - kn^2)^2 = (x^2y)^2 - 2 \cdot x^2y \cdot kn^2 + (kn^2)^2 = x^4y^2 - 2x^2ykn^2 + k^2n^4$ 13. $(y^3x + m^2n^3)^2 = (y^3x)^2 + 2 \cdot y^3x \cdot m^2n^3 + (m^2n^3)^2 = y^6x^2 + 2y^3xm^2n^3 + m^4n^6$