Упр.580 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) 0,42ac3*1*3/7*a4c2;
2) 1,2xyz*2*1/6*x5y6;
3) -2*1/3*m2np3*(3/7np4)2;
4) (1*1/2*x2y3)5*16/27*x8y2. Выполните возведение в квадрат:
1) (10a2-7ab2)2;
2) (0,8b3+0,2b2c4)2;
3) (30m3n+0,04n2)2;
4) (0,5x4y5-20y6)2;
5) (1*1/3*a2b + 2*1/4*ab2)2;
6) (2*1/3*x3y2-9/14*y8x)2;
7) (15m9 + 5/6*m3)2;
8) (3*1/8*x8y10 + 16/25*x2y6)2.

1. $$0{,}42ac^3 \cdot 1\frac{3}{7}a^4c^2=\frac{42}{100}ac^3\cdot \frac{10}{7}a^4c^2=\frac{6}{10}a^5c^5=0{,}6a^5c^5.$$

2. $$1{,}2xyz\cdot 2\frac{1}{6}x^5y^6=\frac{12}{10}xyz\cdot \frac{13}{6}x^5y^6=\frac{2\cdot 13}{10}x^6y^7z=2{,}6x^6y^7z.$$

3. $$-2\frac{1}{3}m^2np^3\cdot \left(\frac{3}{7}np^4\right)^2=-\frac{7}{3}m^2np^3\cdot \frac{9}{49}n^2p^8=-\frac{7\cdot 9}{3\cdot 49}m^2n^3p^{11}=-\frac{3}{7}m^2n^3p^{11}.$$

4. $$\left(1\frac{1}{2}x^2y^3\right)^5\cdot \frac{16}{27}x^8y^2=\left(\frac{3}{2}x^2y^3\right)^5\cdot \frac{2^4}{3^3}x^8y^2$$
   $$=\frac{3^5}{2^5}x^{10}y^{15}\cdot \frac{2^4}{3^3}x^8y^2=\frac{3^2}{2}x^{18}y^{17}=4{,}5x^{18}y^{17}.$$

5. $$\left(10a^2-7ab^2\right)^2=100a^4-140a^3b^2+49a^2b^4.$$

6. $$\left(0{,}8b^3+0{,}2b^2c^4\right)^2=0{,}64b^6+0{,}32b^5c^4+0{,}04b^4c^8.$$

7. $$\left(30m^3n+0{,}04n^2\right)^2=900m^6n^2+2{,}4m^3n^3+0{,}0016n^4.$$

8. $$\left(0{,}5x^4y^5-20y^6\right)^2=0{,}25x^8y^{10}-20x^4y^{11}+400y^{12}.$$

9. $$\left(1\frac{1}{3}a^2b+2\frac{1}{4}ab^2\right)^2=\left(\frac{4}{3}a^2b+\frac{9}{4}ab^2\right)^2$$
   $$=\frac{16}{9}a^4b^2+6a^3b^3+\frac{81}{16}a^2b^4.$$

10. $$\left(2\frac{1}{3}x^3y^2-\frac{9}{14}y^8x\right)^2=\left(\frac{7}{3}x^3y^2-\frac{9}{14}xy^8\right)^2$$
    $$=\frac{49}{9}x^6y^4-3x^4y^{10}+\frac{81}{196}x^2y^{16}.$$

11. $$\left(15m^9+\frac{5}{6}m^3\right)^2=225m^{18}+25m^{12}+\frac{25}{36}m^6.$$

12. $$\left(3\frac{1}{8}x^8y^{10}+\frac{16}{25}x^2y^6\right)^2=\left(\frac{25}{8}x^8y^{10}+\frac{16}{25}x^2y^6\right)^2$$
    $$=\frac{625}{64}x^{16}y^{20}+4x^{10}y^{16}+\frac{256}{625}x^4y^{12}.$$

Ответ

1) $$0{,}6a^5c^5$$; 2) $$2{,}6x^6y^7z$$; 3) $$-\frac{3}{7}m^2n^3p^{11}$$; 4) $$4{,}5x^{18}y^{17}$$; 5) $$100a^4-140a^3b^2+49a^2b^4$$; 6) $$0{,}64b^6+0{,}32b^5c^4+0{,}04b^4c^8$$; 7) $$900m^6n^2+2{,}4m^3n^3+0{,}0016n^4$$; 8) $$0{,}25x^8y^{10}-20x^4y^{11}+400y^{12}$$; 9) $$\frac{16}{9}a^4b^2+6a^3b^3+\frac{81}{16}a^2b^4$$; 10) $$\frac{49}{9}x^6y^4-3x^4y^{10}+\frac{81}{196}x^2y^{16}$$; 11) $$225m^{18}+25m^{12}+\frac{25}{36}m^6$$; 12) $$\frac{625}{64}x^{16}y^{20}+4x^{10}y^{16}+\frac{256}{625}x^4y^{12}$$.