Задание 1 Параграф 19 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 7 класс (Алгебра)

Разложите на множители:

1. $$7a^2-7b^2$$;
2. $$3y^2-27y$$;
3. $$m^5-m^3$$;
4. $$\frac{49}{64}x^2y^3z^6-0{,}04yz^8$$;
5. $$9a^2b^2-6ab^2+b^2$$;
6. $$-3m^3+6m^2n-3mn^2$$;
7. $$4b^2c-20abc+25a^2c$$;
8. $$16x-2x^4$$;
9. $$3a^5+375a^2$$;
10. $$a^4-10000$$.

1. $$7a^2-7b^2=7(a^2-b^2)=7(a-b)(a+b)$$
2. $$3y^2-27y=3y(y-9)$$
3. $$m^5-m^3=m^3(m^2-1)=m^3(m-1)(m+1)$$
4. $$\frac{49}{64}x^2y^3z^6-0{,}04yz^8=yz^6\left(\frac{49}{64}x^2y^2-0{,}04z^2\right)$$
   $$=yz^6\left(\frac78xy-0{,}2z\right)\left(\frac78xy+0{,}2z\right)$$
5. $$9a^2b^2-6ab^2+b^2=b^2(9a^2-6a+1)=b^2(3a-1)^2$$
6. $$-3m^3+6m^2n-3mn^2=-3m(m^2-2mn+n^2)=-3m(m-n)^2$$
7. $$4b^2c-20abc+25a^2c=c(4b^2-20ab+25a^2)=c(2b-5a)^2$$
8. $$16x-2x^4=2x(8-x^3)=2x(2-x)(4+2x+x^2)$$
9. $$3a^5+375a^2=3a^2(a^3+125)=3a^2(a+5)(a^2-5a+25)$$
10. $$a^4-10000=(a^2-100)(a^2+100)=(a-10)(a+10)(a^2+100)$$

Ответ

$$7(a-b)(a+b);\ 3y(y-9);\ m^3(m-1)(m+1);\ yz^6\left(\frac78xy-0{,}2z\right)\left(\frac78xy+0{,}2z\right);$$
$$b^2(3a-1)^2;\ -3m(m-n)^2;\ c(2b-5a)^2;\ 2x(2-x)(4+2x+x^2);$$
$$3a^2(a+5)(a^2-5a+25);\ (a-10)(a+10)(a^2+100)$$