Упр.128 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (x-5)^2-7;
2) 6y+(y-3)^2;
3) (4a-5b)^2-16a(a-3b);
4) (4m+3n)^2+(2m-6n)^2;
5) x(x-2)-(x-3)^2;
6) (8p-q)^2-(4p-q)(16p+3q);
7) y(3y-2)^2-9y(4+y)^2;
8) (x+4)^2-(x-2)(x+2);
9) (8a-3b)(8a+3b)-(6a-5b)^2;
10) (m-3)(m+4)-(m+2)^2+(4-m)(m+4).

1. $$ (x-5)^2-7=x^2-10x+25-7=x^2-10x+18 $$
2. $$ 6y+(y-3)^2=6y+y^2-6y+9=y^2+9 $$
3. $$ (4a-5b)^2-16a(a-3b)=16a^2-40ab+25b^2-16a^2+48ab=25b^2+8ab $$
4. $$ (4m+3n)^2+(2m-6n)^2=16m^2+24mn+9n^2+4m^2-24mn+36n^2=20m^2+45n^2 $$
5. $$ x(x-2)-(x-3)^2=x^2-2x-(x^2-6x+9)=x^2-2x-x^2+6x-9=4x-9 $$
6. $$ (8p-q)^2-(4p-q)(16p+3q)=64p^2-16pq+q^2-(64p^2+12pq-16pq-3q^2) $$
   $$ =64p^2-16pq+q^2-64p^2+4pq+3q^2=4q^2-12pq $$
7. $$ y(3y-2)^2-9y(4+y)^2=y(9y^2-12y+4)-9y(y^2+8y+16) $$
   $$ =9y^3-12y^2+4y-9y^3-72y^2-144y=-84y^2-140y $$
8. $$ (x+4)^2-(x-2)(x+2)=x^2+8x+16-(x^2-4)=x^2+8x+16-x^2+4=8x+20 $$
9. $$ (8a-3b)(8a+3b)-(6a-5b)^2=64a^2-9b^2-(36a^2-60ab+25b^2) $$
   $$ =64a^2-9b^2-36a^2+60ab-25b^2=28a^2+60ab-34b^2 $$
10. $$ (m-3)(m+4)-(m+2)^2+(4-m)(m+4)=m^2+m-12-(m^2+4m+4)+(16-m^2) $$
    $$ =m^2+m-12-m^2-4m-4+16-m^2=-m^2-3m $$

Ответ

1. $$x^2-10x+18$$
2. $$y^2+9$$
3. $$25b^2+8ab$$
4. $$20m^2+45n^2$$
5. $$4x-9$$
6. $$4q^2-12pq$$
7. $$-84y^2-140y$$
8. $$8x+20$$
9. $$28a^2+60ab-34b^2$$
10. $$-m^2-3m$$