Упр.14.3 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) a^3+a^2+a+1;
2) x^5-3x^3+4x^2-12;
3) c^6-10c^4-5c^2+50;
4) y^3-18+6y^2-3y;
5) a^2-ab+ac-bc;
6) 20a^3 bc-28ac^2+15a^2 b^2-21bc;
7) x^2 y^2+xy+axy+a;
8) 24x^6-44x^4 y-18x^2 y^3+33y^4.

1. $$a^3+a^2+a+1=a^2(a+1)+(a+1)=(a+1)(a^2+1).$$
2. $$x^5-3x^3+4x^2-12=x^3(x^2-3)+4(x^2-3)=(x^2-3)(x^3+4).$$
3. $$c^6-10c^4-5c^2+50=c^4(c^2-10)-5(c^2-10)=(c^2-10)(c^4-5).$$
4. $$y^3-18+6y^2-3y=(y^3+6y^2)-(3y+18)=y^2(y+6)-3(y+6)=(y+6)(y^2-3).$$
5. $$a^2-ab+ac-bc=a(a-b)+c(a-b)=(a-b)(a+c).$$
6. $$20a^3bc-28ac^2+15a^2b^2-21bc=4ac(5a^2b-7c)+3b(5a^2b-7c)=(5a^2b-7c)(4ac+3b).$$
7. $$x^2y^2+xy+axy+a=xy(xy+1)+a(xy+1)=(xy+1)(xy+a).$$
8. $$24x^6-44x^4y-18x^2y^3+33y^4=4x^4(6x^2-11y)-3y^3(6x^2-11y)=(6x^2-11y)(4x^4-3y^3).$$

Ответ

1) $$(a+1)(a^2+1);$$
2) $$(x^2-3)(x^3+4);$$
3) $$(c^2-10)(c^4-5);$$
4) $$(y+6)(y^2-3);$$
5) $$(a-b)(a+c);$$
6) $$(5a^2b-7c)(4ac+3b);$$
7) $$(xy+1)(xy+a);$$
8) $$(6x^2-11y)(4x^4-3y^3).$$