Упр.19.4 ГДЗ Мерзляк Поляков 7 класс (Алгебра)
1) x^3-1; 4) 1/8 a^3+b^3; 7) a^3-b^15 c^18;
2) 27+a^3; 5) a^6-8; 8) 125c^3 d^3+0,008b^3;
3) 216-y^3; 6) a^3 b^3-c^3; 9) 64/729 x^3-27/1000 y^6.
$$x^3-1=x^3-1^3=(x-1)(x^2+x+1)$$
$$27+a^3=3^3+a^3=(a+3)(a^2-3a+9)$$
$$216-y^3=6^3-y^3=(6-y)(36+6y+y^2)$$
$$\frac18 a^3+b^3=\left(\frac12 a\right)^3+b^3=\left(\frac12 a+b\right)\left(\frac14 a^2-\frac12 ab+b^2\right)$$
$$a^6-8=(a^2)^3-2^3=(a^2-2)(a^4+2a^2+4)$$
$$a^3b^3-c^3=(ab)^3-c^3=(ab-c)(a^2b^2+abc+c^2)$$
$$a^3-b^{15}c^{18}=a^3-(b^5)^3(c^6)^3=(a-b^5c^6)(a^2+ab^5c^6+b^{10}c^{12})$$
$$125c^3d^3+0{,}008b^3=(5cd)^3+(0{,}2b)^3$$
$$=(5cd+0{,}2b)(25c^2d^2-bcd+0{,}04b^2)$$
$$\frac{64}{729}x^3-\frac{27}{1000}y^6=\left(\frac49x\right)^3-\left(\frac3{10}y^2\right)^3$$
$$=\left(\frac49x-\frac3{10}y^2\right)\left(\frac{16}{81}x^2+\frac{2}{15}xy^2+\frac9{100}y^4\right)$$
Ответ
1) $$(x-1)(x^2+x+1)$$
2) $$(a+3)(a^2-3a+9)$$
3) $$(6-y)(36+6y+y^2)$$
4) $$\left(\frac12 a+b\right)\left(\frac14 a^2-\frac12 ab+b^2\right)$$
5) $$(a^2-2)(a^4+2a^2+4)$$
6) $$(ab-c)(a^2b^2+abc+c^2)$$
7) $$(a-b^5c^6)(a^2+ab^5c^6+b^{10}c^{12})$$
8) $$(5cd+0{,}2b)(25c^2d^2-bcd+0{,}04b^2)$$
9) $$\left(\frac49x-\frac3{10}y^2\right)\left(\frac{16}{81}x^2+\frac{2}{15}xy^2+\frac9{100}y^4\right)$$
