Упр.19.11 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x+1)(x^2-x+1)+(2-x)(4+2x+x^2 );
2) (x-4)(x^2+4x+16)-x(x-5)(x+5);
3) a(a-3)^2-(a+3)(a^2-3a+9);
4) (a-1)(a+1)(a^2-a+1)(a^2+a+1)(a^6+1)(a^12+1).

1. $$ (x+1)(x^2-x+1)+(2-x)(4+2x+x^2) $$
   $$ = (x^3+1)+(8-x^3)=9 $$

2. $$ (x-4)(x^2+4x+16)-x(x-5)(x+5) $$
   $$ = (x^3-64)-x(x^2-25) $$
   $$ = x^3-64-x^3+25x=25x-64 $$

3. $$ a(a-3)^2-(a+3)(a^2-3a+9) $$
   $$ = a(a^2-6a+9)-(a^3+27) $$
   $$ = a^3-6a^2+9a-a^3-27 $$
   $$ = -6a^2+9a-27 $$

4. $$ (a-1)(a+1)(a^2-a+1)(a^2+a+1)(a^6+1)(a^{12}+1) $$
   $$ = (a^2-1)(a^2+a+1)(a^2-a+1)(a^6+1)(a^{12}+1) $$
   $$ = (a^3-1)(a^3+1)(a^6+1)(a^{12}+1) $$
   $$ = (a^6-1)(a^6+1)(a^{12}+1) $$
   $$ = (a^{12}-1)(a^{12}+1)=a^{24}-1 $$

Ответ

1) $$9$$;
2) $$25x-64$$;
3) $$-6a^2+9a-27$$;
4) $$a^{24}-1$$.