Упр.104 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (x — 2)(x — 11) — 2x(4 — 3x);
2) (a + 6)(a — 3) + (a — 4)(a + 5);
3) (y — 8)(2y — 1) — (3y + 1)(5y — 2);
4) (3m — 4n)(3m + 5n) — (4,5m — n)(2m + 4n);
5) (x^2 + 2y)(x^3 + 7y) — 6x^3 (x^2 — 3y).

1. $$\begin{aligned}
   (x-2)(x-11)-2x(4-3x) &= x^2-11x-2x+22-8x+6x^2 \\
   &= 7x^2-21x+22.
   \end{aligned}$$

2. $$\begin{aligned}
   (a+6)(a-3)+(a-4)(a+5) &= a^2-3a+6a-18+a^2+5a-4a-20 \\
   &= 2a^2+4a-38.
   \end{aligned}$$

3. $$\begin{aligned}
   (y-8)(2y-1)-(3y+1)(5y-2) &= 2y^2-y-16y+8-(15y^2-6y+5y-2) \\
   &= 2y^2-17y+8-15y^2+y+2 \\
   &= -13y^2-16y+10.
   \end{aligned}$$

4. $$\begin{aligned}
   (3m-4n)(3m+5n)-(4{,}5m-n)(2m+4n) &= 9m^2+15mn-12mn-20n^2 \\
   &\quad -(9m^2+18mn-2mn-4n^2) \\
   &= 9m^2+3mn-20n^2-9m^2-16mn+4n^2 \\
   &= -13mn-16n^2.
   \end{aligned}$$

5. $$\begin{aligned}
   (x^2+2y)(x^3+7y)-6x^3(x^2-3y) &= x^5+7x^2y+2x^3y+14y^2-6x^5+18x^3y \\
   &= -5x^5+20x^3y+7x^2y+14y^2.
   \end{aligned}$$

Ответ

1) $$7x^2-21x+22$$;
2) $$2a^2+4a-38$$;
3) $$-13y^2-16y+10$$;
4) $$-13mn-16n^2$$;
5) $$-5x^5+20x^3y+7x^2y+14y^2$$.