Упр.4.47 ГДЗ Мордкович 8 класс (Алгебра)

а)

$$c^2-cd+d^2-\frac{c^3-d^3}{c+d} = \frac{(c^2-cd+d^2)(c+d)-c^3+d^3}{c+d}$$

$$(c^2-cd+d^2)(c+d)=c^3+d^3$$

$$\frac{c^3+d^3-c^3+d^3}{c+d}=\frac{2d^3}{c+d}$$

б)

$$\frac{a^3-b^3}{a^2-ab+b^2}-a-b = \frac{a^3-b^3-(a+b)(a^2-ab+b^2)}{a^2-ab+b^2}$$

$$(a+b)(a^2-ab+b^2)=a^3+b^3$$

$$\frac{a^3-b^3-a^3-b^3}{a^2-ab+b^2} = \frac{-2b^3}{a^2-ab+b^2}$$

в)

$$\frac{m^3+n^3}{m-n}-m^2-mn-n^2 = \frac{m^3+n^3-(m^2+mn+n^2)(m-n)}{m-n}$$

$$(m^2+mn+n^2)(m-n)=m^3-n^3$$

$$\frac{m^3+n^3-m^3+n^3}{m-n} = \frac{2n^3}{m-n}$$

г)

$$\frac{x^3+y^3}{x^2+xy+y^2}+x-y = \frac{x^3+y^3+(x-y)(x^2+xy+y^2)}{x^2+xy+y^2}$$

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

$$\frac{x^3+y^3+x^3-y^3}{x^2+xy+y^2} = \frac{2x^3}{x^2+xy+y^2}$$

Ответ

а) $$\frac{2d^3}{c+d}$$; б) $$\frac{-2b^3}{a^2-ab+b^2}$$; в) $$\frac{2n^3}{m-n}$$; г) $$\frac{2x^3}{x^2+xy+y^2}$$.