Упр.116 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) ab-ac+yb-yc;
2) 3x+3y-bx-by;
3) 4n-nc-4+c;
4) x^7+x^3-4x^4-4;
5) 6mn-3m+2n-1;
6) 4a^4-5a^3 y-8a+10y;
7) a^2 b^2-a+ab^2-1;
8) xa-xb^2-ya+zb^2-za+yb^2.

1. $$ab-ac+yb-yc=a(b-c)+y(b-c)=(b-c)(a+y)$$
2. $$3x+3y-bx-by=3(x+y)-b(x+y)=(x+y)(3-b)$$
3. $$4n-nc-4+c=n(4-c)-(4-c)=(4-c)(n-1)$$
4. $$x^7+x^3-4x^4-4=x^3(x^4+1)-4(x^4+1)=(x^4+1)(x^3-4)$$
5. $$6mn-3m+2n-1=3m(2n-1)+(2n-1)=(2n-1)(3m+1)$$
6. $$4a^4-5a^3y-8a+10y=a^3(4a-5y)-2(4a-5y)=(4a-5y)(a^3-2)$$
7. $$a^2b^2-a+ab^2-1=(a^2b^2+ab^2)-(a+1)=ab^2(a+1)-(a+1)=(a+1)(ab^2-1)$$
8. $$xa-xb^2-ya+zb^2-za+yb^2=(xa-ya)-(xb^2-yb^2)-z(a-b^2)$$
   $$=a(x-y)-b^2(x-y)-z(a-b^2)=(x-y)(a-b^2)-z(a-b^2)$$
   $$=(a-b^2)(x-y-z)$$

Ответ

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