Упр.8 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) 3a^3-27a; 5)-75b^6+30b^4-3b^2;
2) 3x^4-3x^2 y^2; 6) 2x^6-16y^9;
3) 4m^2 n^4-64m^2 p^4; 7) x+4y+x^2-16y^2;
4) 2x^2+24xy+72y^2; 8) x^2 y^5-y^5-x^2 y^3+y^3.

1. $$3a^3-27a=3a(a^2-9)=3a(a-3)(a+3)$$
2. $$3x^4-3x^2y^2=3x^2(x^2-y^2)=3x^2(x-y)(x+y)$$
3. $$4m^2n^4-64m^2p^4=4m^2(n^4-16p^4)=4m^2(n^2-4p^2)(n^2+4p^2)$$
   $$=4m^2(n-2p)(n+2p)(n^2+4p^2)$$
4. $$2x^2+24xy+72y^2=2(x^2+12xy+36y^2)=2(x+6y)^2$$
5. $$-75b^6+30b^4-3b^2=-3b^2(25b^4-10b^2+1)=-3b^2(5b^2-1)^2$$
6. $$2x^6-16y^9=2(x^6-8y^9)=2(x^6-(2y^3)^3)$$
   $$=2(x^2-2y^3)(x^4+2x^2y^3+4y^6)$$
7. $$x+4y+x^2-16y^2=(x+4y)+(x^2-16y^2)$$
   $$=(x+4y)+(x-4y)(x+4y)$$
   $$=(x+4y)(1+x-4y)$$
8. $$x^2y^5-y^5-x^2y^3+y^3=y^5(x^2-1)-y^3(x^2-1)$$
   $$=(x^2-1)(y^5-y^3)=y^3(x^2-1)(y^2-1)$$
   $$=y^3(x-1)(x+1)(y-1)(y+1)$$

Ответ

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