Упр.17.4 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

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

1. $$\left(a+8\right)^2=a^2+2\cdot a\cdot 8+8^2=a^2+16a+64$$
2. $$\left(b-2\right)^2=b^2-2\cdot b\cdot 2+2^2=b^2-4b+4$$
3. $$\left(7+c\right)^2=7^2+2\cdot 7\cdot c+c^2=49+14c+c^2$$
4. $$\left(6-d\right)^2=6^2-2\cdot 6\cdot d+d^2=36-12d+d^2$$
5. $$\left(2m+1\right)^2=\left(2m\right)^2+2\cdot 2m\cdot 1+1^2=4m^2+4m+1$$
6. $$\left(4x-3\right)^2=\left(4x\right)^2-2\cdot 4x\cdot 3+3^2=16x^2-24x+9$$
7. $$\left(5m-4n\right)^2=\left(5m\right)^2-2\cdot 5m\cdot 4n+\left(4n\right)^2=25m^2-40mn+16n^2$$
8. $$\left(10c+7d\right)^2=\left(10c\right)^2+2\cdot 10c\cdot 7d+\left(7d\right)^2=100c^2+140cd+49d^2$$
9. $$\left(4x-\frac{1}{8}y\right)^2=\left(4x\right)^2-2\cdot 4x\cdot \frac{1}{8}y+\left(\frac{1}{8}y\right)^2=16x^2-xy+\frac{1}{64}y^2$$
10. $$\left(0{,}3a+0{,}9b\right)^2=\left(0{,}3a\right)^2+2\cdot 0{,}3a\cdot 0{,}9b+\left(0{,}9b\right)^2=0{,}09a^2+0{,}54ab+0{,}81b^2$$
11. $$\left(c^2-6\right)^2=\left(c^2\right)^2-2\cdot c^2\cdot 6+6^2=c^4-12c^2+36$$
12. $$\left(15+k^2\right)^2=15^2+2\cdot 15\cdot k^2+\left(k^2\right)^2=225+30k^2+k^4$$
13. $$\left(m^2-3n\right)^2=\left(m^2\right)^2-2\cdot m^2\cdot 3n+\left(3n\right)^2=m^4-6m^2n+9n^2$$
14. $$\left(m^4-n^3\right)^2=\left(m^4\right)^2-2\cdot m^4\cdot n^3+\left(n^3\right)^2=m^8-2m^4n^3+n^6$$
15. $$\left(5a^4-2a^7\right)^2=\left(5a^4\right)^2-2\cdot 5a^4\cdot 2a^7+\left(2a^7\right)^2=25a^8-20a^{11}+4a^{14}$$

Ответ

1) $$a^2+16a+64$$; 2) $$b^2-4b+4$$; 3) $$49+14c+c^2$$; 4) $$36-12d+d^2$$; 5) $$4m^2+4m+1$$; 6) $$16x^2-24x+9$$; 7) $$25m^2-40mn+16n^2$$; 8) $$100c^2+140cd+49d^2$$; 9) $$16x^2-xy+\frac{1}{64}y^2$$; 10) $$0{,}09a^2+0{,}54ab+0{,}81b^2$$; 11) $$c^4-12c^2+36$$; 12) $$225+30k^2+k^4$$; 13) $$m^4-6m^2n+9n^2$$; 14) $$m^8-2m^4n^3+n^6$$; 15) $$25a^8-20a^{11}+4a^{14}$$.