Упр.17.15 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 6(1-2c)^2; 2)-12(x+1/3 y)^2;
3) a(a-6b)^2; 4) 5b(b^2+7b)^2;
5) (a+3) (a-4)^2; 6) (2x+4)^2 (x-8);
7) (a-5)^2 (a+5)^2; 8) (3x+4y)^2 (3x-4y)^2;
9) (x+y-1)^2; 10) (a^2-b-c^2 )^2.

1. $$6(1-2c)^2=6(1-4c+4c^2)=6-24c+24c^2.$$
2. $$ -12\left(x+\frac13 y\right)^2 =-12\left(x^2+\frac23 xy+\frac19 y^2\right) =-12x^2-8xy-\frac43 y^2. $$
3. $$a(a-6b)^2=a(a^2-12ab+36b^2)=a^3-12a^2b+36ab^2.$$
4. $$5b(b^2+7b)^2=5b(b^4+14b^3+49b^2)=5b^5+70b^4+245b^3.$$
5. $$ (a+3)(a-4)^2=(a+3)(a^2-8a+16) =a^3-5a^2-8a+48. $$
6. $$ (2x+4)^2(x-8)=(4x^2+16x+16)(x-8) =4x^3-16x^2-112x-128. $$
7. $$ (a-5)^2(a+5)^2=\bigl((a-5)(a+5)\bigr)^2=(a^2-25)^2=a^4-50a^2+625. $$
8. $$ (3x+4y)^2(3x-4y)^2=\bigl((3x+4y)(3x-4y)\bigr)^2=(9x^2-16y^2)^2 =81x^4-288x^2y^2+256y^4. $$
9. $$ (x+y-1)^2=(x+y)^2-2(x+y)+1=x^2+y^2+2xy-2x-2y+1. $$
10. $$ (a^2-b-c^2)^2=(a^2-b)^2-2c^2(a^2-b)+c^4 =a^4+b^2+c^4-2a^2b-2a^2c^2+2bc^2. $$

Ответ

1) $$6-24c+24c^2$$

2) $$-12x^2-8xy-\frac43 y^2$$

3) $$a^3-12a^2b+36ab^2$$

4) $$5b^5+70b^4+245b^3$$

5) $$a^3-5a^2-8a+48$$

6) $$4x^3-16x^2-112x-128$$

7) $$a^4-50a^2+625$$

8) $$81x^4-288x^2y^2+256y^4$$

9) $$x^2+y^2+2xy-2x-2y+1$$

10) $$a^4+b^2+c^4-2a^2b-2a^2c^2+2bc^2$$