Упр.127 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (a+2)^2; 9) (x^4 — x^2)^2;
2) (6-x)^2; 10) (y^4 + y^3)^2;
3) (1/2 a + b)^2; 11) (-3a + 4b^3)^2;
4) (3x — 4)^2; 12) (-2 — 5x)^2;
5) (5m + 3n)^2; 13) (1 1/3 m + 3 3/5 n)^2;
6) (0,1a + 10b)^2; 14) (6ab^2 — a^2 b)^2;
7) (6x — 1/3 y)^2; 15) (5a^4 — 2a^2 b^4)^2.
8) (n^2 + 1)^2;

1. $$\left(a+2\right)^2=a^2+2\cdot a\cdot 2+2^2=a^2+4a+4.$$
2. $$\left(6-x\right)^2=6^2-2\cdot 6\cdot x+x^2=36-12x+x^2.$$
3. $$\left(\frac12 a+b\right)^2=\left(\frac12 a\right)^2+2\cdot \frac12 a\cdot b+b^2=\frac14 a^2+ab+b^2.$$
4. $$\left(3x-4\right)^2=(3x)^2-2\cdot 3x\cdot 4+4^2=9x^2-24x+16.$$
5. $$\left(5m+3n\right)^2=(5m)^2+2\cdot 5m\cdot 3n+(3n)^2=25m^2+30mn+9n^2.$$
6. $$\left(0{,}1a+10b\right)^2=(0{,}1a)^2+2\cdot 0{,}1a\cdot 10b+(10b)^2=0{,}01a^2+2ab+100b^2.$$
7. $$\left(6x-\frac13 y\right)^2=(6x)^2-2\cdot 6x\cdot \frac13 y+\left(\frac13 y\right)^2=36x^2-4xy+\frac19 y^2.$$
8. $$\left(n^2+1\right)^2=(n^2)^2+2\cdot n^2\cdot 1+1^2=n^4+2n^2+1.$$
9. $$\left(x^4-x^2\right)^2=(x^4)^2-2\cdot x^4\cdot x^2+(x^2)^2=x^8-2x^6+x^4.$$
10. $$\left(y^4+y^3\right)^2=(y^4)^2+2\cdot y^4\cdot y^3+(y^3)^2=y^8+2y^7+y^6.$$
11. $$\left(-3a+4b^3\right)^2=(-3a)^2+2\cdot (-3a)\cdot 4b^3+(4b^3)^2=9a^2-24ab^3+16b^6.$$
12. $$\left(-2-5x\right)^2=\left(2+5x\right)^2=2^2+2\cdot 2\cdot 5x+(5x)^2=4+20x+25x^2.$$
13. $$1\frac13=\frac43,\qquad 3\frac35=\frac{18}{5}.$$
    $$\left(1\frac13 m+3\frac35 n\right)^2=\left(\frac43 m+\frac{18}{5}n\right)^2$$
    $$=\left(\frac43 m\right)^2+2\cdot \frac43 m\cdot \frac{18}{5}n+\left(\frac{18}{5}n\right)^2$$
    $$=\frac{16}{9}m^2+\frac{48}{5}mn+\frac{324}{25}n^2.$$
14. $$\left(6ab^2-a^2b\right)^2=(6ab^2)^2-2\cdot 6ab^2\cdot a^2b+(a^2b)^2$$
    $$=36a^2b^4-12a^3b^3+a^4b^2.$$
15. $$\left(5a^4-2a^2b^4\right)^2=(5a^4)^2-2\cdot 5a^4\cdot 2a^2b^4+(2a^2b^4)^2$$
    $$=25a^8-20a^6b^4+4a^4b^8.$$

Ответ

1) $$a^2+4a+4$$; 2) $$36-12x+x^2$$; 3) $$\frac14 a^2+ab+b^2$$; 4) $$9x^2-24x+16$$; 5) $$25m^2+30mn+9n^2$$; 6) $$0{,}01a^2+2ab+100b^2$$; 7) $$36x^2-4xy+\frac19 y^2$$; 8) $$n^4+2n^2+1$$; 9) $$x^8-2x^6+x^4$$; 10) $$y^8+2y^7+y^6$$; 11) $$9a^2-24ab^3+16b^6$$; 12) $$4+20x+25x^2$$; 13) $$\frac{16}{9}m^2+\frac{48}{5}mn+\frac{324}{25}n^2$$; 14) $$36a^2b^4-12a^3b^3+a^4b^2$$; 15) $$25a^8-20a^6b^4+4a^4b^8$$.