Упр.17 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1) (8х — у2)(3х + у2);
2) (2m2n — 5mn2)(3mn2 — 4m2n);
3) (5ху2 — 2х2у)(2х2у + 5ху2);
4) (1/2*a3 + b2)(b2-1/2*a3);
5) (а6 — а3b3 + b6)(a3 + b2);
6) (9m4 + 3m2n2 + n4)(3m2 — n2).

1. $$ (8x-y^2)(3x+y^2)=8x\cdot 3x+8x\cdot y^2-y^2\cdot 3x-y^2\cdot y^2 $$

   $$ =24x^2+8xy^2-3xy^2-y^4=24x^2+5xy^2-y^4 $$

2. $$ (2m^2n-5mn^2)(3mn^2-4m^2n) $$

   $$ =2m^2n\cdot 3mn^2-2m^2n\cdot 4m^2n-5mn^2\cdot 3mn^2+5mn^2\cdot 4m^2n $$

   $$ =6m^3n^3-8m^4n^2-15m^2n^4+20m^3n^3 $$

   $$ =26m^3n^3-8m^4n^2-15m^2n^4 $$

3. $$ (5xy^2-2x^2y)(2x^2y+5xy^2) $$

   $$ =5xy^2\cdot 2x^2y+5xy^2\cdot 5xy^2-2x^2y\cdot 2x^2y-2x^2y\cdot 5xy^2 $$

   $$ =10x^3y^3+25x^2y^4-4x^4y^2-10x^3y^3 $$

   $$ =25x^2y^4-4x^4y^2 $$

4. $$ \left(\frac12 a^3+b^2\right)\left(b^2-\frac12 a^3\right) $$

   $$ =(b^2)^2-\left(\frac12 a^3\right)^2 $$

   $$ =b^4-\frac14 a^6 $$

5. $$ (a^6-a^3b^3+b^6)(a^3+b^3) $$

   $$ =(a^3)^3+(b^3)^3 $$

   $$ =a^9+b^9 $$

6. $$ (9m^4+3m^2n^2+n^4)(3m^2-n^2) $$

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

   $$ =27m^6-n^6 $$

Ответ

1) $$24x^2+5xy^2-y^4$$; 2) $$26m^3n^3-8m^4n^2-15m^2n^4$$; 3) $$25x^2y^4-4x^4y^2$$; 4) $$b^4-\frac14 a^6$$; 5) $$a^9+b^9$$; 6) $$27m^6-n^6$$.