16.14. Выполните возведение в квадрат: 1) (10a^2 - 7ab^2)^2; 2) (0,8b^3 + 0,2b^2c^4)^2; 3) (30m^3n + 0,04n^2)^2; 4) (0,5x^4y^5 - 20y^6)^2; 5) (1 1/3a^2b + 2 1/4ab^2)^2; 6) (2 1/3x^3y^2 - 9/14y^8x)^2; 7) (15m^9 + 5/6m^3)^2; 8) (3 1/8x^8y^10 + 16/25x^2y^6)^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) $(10a^2 - 7ab^2)^2 = (10a^2)^2 - 2 \cdot 10a^2 \cdot 7ab^2 + (7ab^2)^2 = 100a^4 - 140a^3b^2 + 49a^2b^4$ 2) $(0,8b^3 + 0,2b^2c^4)^2 = (0,8b^3)^2 + 2 \cdot 0,8b^3 \cdot 0,2b^2c^4 + (0,2b^2c^4)^2 = 0,64b^6 + 0,32b^5c^4 + 0,04b^4c^8$ 3) $(30m^3n + 0,04n^2)^2 = (30m^3n)^2 + 2 \cdot 30m^3n \cdot 0,04n^2 + (0,04n^2)^2 = 900m^6n^2 + 2,4m^3n^3 + 0,0016n^4$ 4) $(0,5x^4y^5 - 20y^6)^2 = (0,5x^4y^5)^2 - 2 \cdot 0,5x^4y^5 \cdot 20y^6 + (20y^6)^2 = 0,25x^8y^{10} - 20x^4y^{11} + 400y^{12}$ 5) $(1\frac{1}{3}a^2b + 2\frac{1}{4}ab^2)^2 = (\frac{4}{3}a^2b + \frac{9}{4}ab^2)^2 = (\frac{4}{3}a^2b)^2 + 2 \cdot \frac{4}{3}a^2b \cdot \frac{9}{4}ab^2 + (\frac{9}{4}ab^2)^2 = \frac{16}{9}a^4b^2 + 6a^3b^3 + \frac{81}{16}a^2b^4 = 1\frac{7}{9}a^4b^2 + 6a^3b^3 + 5\frac{1}{16}a^2b^4$ 6) $(2\frac{1}{3}x^3y^2 - \frac{9}{14}y^8x)^2 = (\frac{7}{3}x^3y^2 - \frac{9}{14}xy^8)^2 = (\frac{7}{3}x^3y^2)^2 - 2 \cdot \frac{7}{3}x^3y^2 \cdot \frac{9}{14}xy^8 + (\frac{9}{14}xy^8)^2 = \frac{49}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16} = 5\frac{4}{9}x^6y^4 - 3x^4y^{10} + \frac{81}{196}x^2y^{16}$ 7) $(15m^9 + \frac{5}{6}m^3)^2 = (15m^9)^2 + 2 \cdot 15m^9 \cdot \frac{5}{6}m^3 + (\frac{5}{6}m^3)^2 = 225m^{18} + 25m^{12} + \frac{25}{36}m^6$ 8) $(3\frac{1}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2 = (\frac{25}{8}x^8y^{10} + \frac{16}{25}x^2y^6)^2 = (\frac{25}{8}x^8y^{10})^2 + 2 \cdot \frac{25}{8}x^8y^{10} \cdot \frac{16}{25}x^2y^6 + (\frac{16}{25}x^2y^6)^2 = \frac{625}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12} = 9\frac{49}{64}x^{16}y^{20} + 4x^{10}y^{16} + \frac{256}{625}x^4y^{12}$