Упр.17.16 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (0,02p^3 k+20p^2 k^4 )^2; 2) (1 1/6 mn-4/21 m^2 n^5 )^2;
3)-15(1/3 a-1/5 b)^2; 4) 7x(x^3-2x)^2;
5) (5y-2)^2 (2y+1); 6) (10p-k)^2 (10p+k)^2;
7) (m-2n+3)^2.

1. $$\left(0{,}02p^3k+20p^2k^4\right)^2=\left(0{,}02p^3k\right)^2+2\cdot 0{,}02p^3k\cdot 20p^2k^4+\left(20p^2k^4\right)^2$$
   $$=0{,}0004p^6k^2+0{,}8p^5k^5+400p^4k^8.$$
2. $$\left(1\frac{1}{6}mn-\frac{4}{21}m^2n^5\right)^2=\left(\frac{7}{6}mn-\frac{4}{21}m^2n^5\right)^2$$
   $$=\left(\frac{7}{6}mn\right)^2-2\cdot \frac{7}{6}mn\cdot \frac{4}{21}m^2n^5+\left(\frac{4}{21}m^2n^5\right)^2$$
   $$=\frac{49}{36}m^2n^2-\frac{4}{9}m^3n^6+\frac{16}{441}m^4n^{10}.$$
3. $$-15\left(\frac{1}{3}a-\frac{1}{5}b\right)^2=-15\left(\frac{1}{9}a^2-\frac{2}{15}ab+\frac{1}{25}b^2\right)$$
   $$=-\frac{5}{3}a^2+2ab-\frac{3}{5}b^2.$$
4. $$7x(x^3-2x)^2=7x(x^6-4x^4+4x^2)$$
   $$=7x^7-28x^5+28x^3.$$
5. $$\left(5y-2\right)^2(2y+1)=\left(25y^2-20y+4\right)(2y+1)$$
   $$=50y^3+25y^2-40y^2-20y+8y+4$$
   $$=50y^3-15y^2-12y+4.$$
6. $$\left(10p-k\right)^2\left(10p+k\right)^2=\left((10p-k)(10p+k)\right)^2$$
   $$=\left(100p^2-k^2\right)^2$$
   $$=10000p^4-200p^2k^2+k^4.$$
7. $$\left(m-2n+3\right)^2=\left((m-2n)+3\right)^2$$
   $$=(m-2n)^2+6(m-2n)+9$$
   $$=m^2-4mn+4n^2+6m-12n+9.$$

Ответ

1) $$0{,}0004p^6k^2+0{,}8p^5k^5+400p^4k^8$$;
2) $$\frac{49}{36}m^2n^2-\frac{4}{9}m^3n^6+\frac{16}{441}m^4n^{10}$$;
3) $$-\frac{5}{3}a^2+2ab-\frac{3}{5}b^2$$;
4) $$7x^7-28x^5+28x^3$$;
5) $$50y^3-15y^2-12y+4$$;
6) $$10000p^4-200p^2k^2+k^4$$;
7) $$m^2-4mn+4n^2+6m-12n+9$$.