Упр.21.12 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 15cx+2cy-cxy-30c; 3) x^3+x^2 y+x^2+xy;
2) 35a^2-42ab+10a^2 b-12ab^2; 4) mn^4-n^4+mn^3-n^3.

1. $$15cx+2cy-cxy-30c=(15cx-cxy)+(2cy-30c)$$
   $$=cx(15-y)+2c(y-15)=cx(15-y)-2c(15-y)$$
   $$=(15-y)(cx-2c)=c(15-y)(x-2)$$
2. $$35a^2-42ab+10a^2b-12ab^2=(35a^2+10a^2b)-(42ab+12ab^2)$$
   $$=5a^2(7+2b)-6ab(7+2b)$$
   $$=(7+2b)(5a^2-6ab)=a(7+2b)(5a-6b)$$
3. $$x^3+x^2y+x^2+xy=x^2(x+y)+x(x+y)$$
   $$=(x+y)(x^2+x)=x(x+y)(x+1)$$
4. $$mn^4-n^4+mn^3-n^3=n^4(m-1)+n^3(m-1)$$
   $$=(m-1)(n^4+n^3)$$
   $$=n^3(m-1)(n+1)$$

Ответ

1) $$c(15-y)(x-2)$$; 2) $$a(7+2b)(5a-6b)$$; 3) $$x(x+y)(x+1)$$; 4) $$n^3(m-1)(n+1)$$.