Упр.535 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) 6m^4 n+12m^3 n+3m^2 n; 2) 2a^5 b-4a^4 b+2a^3 b;
3) a^2-2ab+b^2-y^2; 4) a^4+2a^2 b^2+b^4-4a^2 b^2.

1. $$6m^4n+12m^3n+3m^2n=3m^2n(2m^2+4m+1).$$
2. $$2a^5b-4a^4b+2a^3b=2a^3b(a^2-2a+1)=2a^3b(a-1)^2.$$
3. $$a^2-2ab+b^2-y^2=(a-b)^2-y^2=(a-b-y)(a-b+y).$$
4. $$a^4+2a^2b^2+b^4-4a^2b^2=a^4-2a^2b^2+b^4=(a^2-b^2)^2=(a-b)^2(a+b)^2.$$

Ответ

1) $$3m^2n(2m^2+4m+1)$$
2) $$2a^3b(a-1)^2$$
3) $$ (a-b-y)(a-b+y) $$
4) $$ (a-b)^2(a+b)^2 $$