Упр.7.64 ГДЗ Дорофеев Суворова 7 класс (Алгебра)

б) а3 — q3;
в) 1 — x3;
г) -x3 + у3;
д) b3 — 1/125;
е) 1/27 — t3.

1. $$p^3-q^3=(p-q)(p^2+pq+q^2)$$

2. $$a^3-8=a^3-2^3=(a-2)(a^2+2a+4)$$

3. $$1-x^3=(1-x)(1+x+x^2)$$

4. $$-x^3+y^3=y^3-x^3=(y-x)(y^2+xy+x^2)$$

5. $$b^3-\frac{1}{125}=b^3-\left(\frac{1}{5}\right)^3=\left(b-\frac{1}{5}\right)\left(b^2+\frac{1}{5}b+\frac{1}{25}\right)$$

6. $$\frac{1}{27}-t^3=\left(\frac{1}{3}\right)^3-t^3=\left(\frac{1}{3}-t\right)\left(\frac{1}{9}+\frac{1}{3}t+t^2\right)$$

Ответ

$$p^3-q^3=(p-q)(p^2+pq+q^2),$$
$$a^3-8=(a-2)(a^2+2a+4),$$
$$1-x^3=(1-x)(1+x+x^2),$$
$$-x^3+y^3=(y-x)(y^2+xy+x^2),$$
$$b^3-\frac{1}{125}=\left(b-\frac{1}{5}\right)\left(b^2+\frac{1}{5}b+\frac{1}{25}\right),$$
$$\frac{1}{27}-t^3=\left(\frac{1}{3}-t\right)\left(\frac{1}{9}+\frac{1}{3}t+t^2\right).$$