Упр.709 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1. $$\left(0{,}02p^3k+20p^2k^4\right)^2=$$
   $$=0{,}0004p^6k^2+0{,}8p^5k^5+400p^4k^8.$$

2. $$\left(1\frac{1}{6}mn-\frac{4}{21}m^2n^5\right)^2=\left(\frac{7}{6}mn-\frac{4}{21}m^2n^5\right)^2=$$
   $$=\frac{49}{36}m^2n^2-\frac{4}{9}m^3n^6+\frac{16}{441}m^4n^{10}.$$

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. $$\left(10p-k\right)^2\left(10p+k\right)^2=\left(\left(10p-k\right)\left(10p+k\right)\right)^2=$$
   $$=\left(100p^2-k^2\right)^2=$$
   $$=10000p^4-200p^2k^2+k^4.$$

1. $$3a^2+6ab+3b^2=3\left(a^2+2ab+b^2\right)=3(a+b)^2.$$

2. $$5m^2+5n^2-10mn=5\left(m^2-2mn+n^2\right)=5(m-n)^2.$$

3. $$-3x^2+12x-12=-3\left(x^2-4x+4\right)=-3(x-2)^2.$$

4. $$-7b^2-14bc-7c^2=-7\left(b^2+2bc+c^2\right)=-7(b+c)^2.$$

5. $$x^2y+14xy^2+49y^3=y\left(x^2+14xy+49y^2\right)=y(x+7y)^2.$$

6. $$-8a^3b+56a^2b^2-98ab^3=-2ab\left(4a^2-28ab+49b^2\right)=-2ab(2a-7b)^2.$$

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) $$10000p^4-200p^2k^2+k^4$$

1) $$3(a+b)^2$$
2) $$5(m-n)^2$$
3) $$-3(x-2)^2$$
4) $$-7(b+c)^2$$
5) $$y(x+7y)^2$$
6) $$-2ab(2a-7b)^2$$