Упр.17.14 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (10a^2-7ab^2 )^2; 5) (1 1/3 a^2 b+2 1/4 ab^2 )^2;
2) (0,8b^3+0,2b^2 c^4 )^2; 6) (2 1/3 x^3 y^2-9/14 y^8 x)^2;
3) (30m^3 n+0,04n^2 )^2; 7) (15m^9+5/6 m^3 )^2;
4) (0,5x^4 y^5-20y^6 )^2; 8) (3 1/8 x^8 y^10+16/25 x^2 y^6 )^2.

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

Ответ

1) $$100a^4-140a^3b^2+49a^2b^4$$
2) $$0{,}64b^6+0{,}32b^5c^4+0{,}04b^4c^8$$
3) $$900m^6n^2+2{,}4m^3n^3+0{,}0016n^4$$
4) $$0{,}25x^8y^{10}-20x^4y^{11}+400y^{12}$$
5) $$\frac{16}{9}a^4b^2+6a^3b^3+\frac{81}{16}a^2b^4$$
6) $$\frac{49}{9}x^6y^4-3x^4y^{10}+\frac{81}{196}x^2y^{16}$$
7) $$225m^{18}+25m^{12}+\frac{25}{36}m^6$$
8) $$\frac{625}{64}x^{16}y^{20}+4x^{10}y^{16}+\frac{256}{625}x^4y^{12}$$