Упр.500 ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (х + 2)(х+ 11) -2х(3-4х);
2) (а + 5)(а — 2) + (а — 4)(а + 6);
3) (у — 9)(3у — 1) — (2у + 1)(5у — 7);
4) (4х- 1)(4г — 3) — (2х- 10)(8х + 1).
Выполните умножение многочленов:
1) (m — n)(m + );
2) (х- 1)(х + 1);
3) (9 -у)(9 + у);
4) (3b — 1)(3b + 1);
5) (10m-7)(10m + 7);
6) (4a — b)(b + 4а);
7) (5b + 1)(1 — 5b);
8) (3х — 5у)(3х + 5у);
9) (13с — 10d)(13c +10d);
10) (8m + 11n)(11n — 8m).

1. $$\begin{aligned}
   (x+2)(x+11)-2x(3-4x) &= x^2+11x+2x+22-6x+8x^2 \\
   &= 9x^2+7x+22
   \end{aligned}$$
2. $$\begin{aligned}
   (a+5)(a-2)+(a-4)(a+6) &= a^2-2a+5a-10+a^2+6a-4a-24 \\
   &= 2a^2+5a-34
   \end{aligned}$$
3. $$\begin{aligned}
   (y-9)(3y-1)-(2y+1)(5y-7) &= 3y^2-y-27y+9-(10y^2-14y+5y-7) \\
   &= 3y^2-28y+9-10y^2+9y+7 \\
   &= -7y^2-19y+16
   \end{aligned}$$
4. $$\begin{aligned}
   (4x-1)(4x-3)-(2x-10)(8x+1) &= 16x^2-12x-4x+3-(16x^2+2x-80x-10) \\
   &= 16x^2-16x+3-16x^2-2x+80x+10 \\
   &= 62x+13
   \end{aligned}$$
5. $$\begin{aligned}
   (m-n)(m+n) &= m^2-n^2
   \end{aligned}$$
6. $$\begin{aligned}
   (x-1)(x+1) &= x^2-1
   \end{aligned}$$
7. $$\begin{aligned}
   (9-y)(9+y) &= 9^2-y^2 = 81-y^2
   \end{aligned}$$
8. $$\begin{aligned}
   (3b-1)(3b+1) &= (3b)^2-1^2 = 9b^2-1
   \end{aligned}$$
9. $$\begin{aligned}
   (10m-7)(10m+7) &= (10m)^2-7^2 = 100m^2-49
   \end{aligned}$$
10. $$\begin{aligned}
    (4a-b)(4a+b) &= (4a)^2-b^2 = 16a^2-b^2
    \end{aligned}$$
11. $$\begin{aligned}
    (5b+1)(1-5b) &= (1+5b)(1-5b) = 1-(5b)^2 = 1-25b^2
    \end{aligned}$$
12. $$\begin{aligned}
    (3x-5y)(3x+5y) &= (3x)^2-(5y)^2 = 9x^2-25y^2
    \end{aligned}$$
13. $$\begin{aligned}
    (13c-10d)(13c+10d) &= (13c)^2-(10d)^2 = 169c^2-100d^2
    \end{aligned}$$
14. $$\begin{aligned}
    (8m+11n)(11n-8m) &= (11n+8m)(11n-8m) \\
    &= (11n)^2-(8m)^2 = 121n^2-64m^2
    \end{aligned}$$

Ответ

1) $$9x^2+7x+22$$; 2) $$2a^2+5a-34$$; 3) $$-7y^2-19y+16$$; 4) $$62x+13$$; 5) $$m^2-n^2$$; 6) $$x^2-1$$; 7) $$81-y^2$$; 8) $$9b^2-1$$; 9) $$100m^2-49$$; 10) $$16a^2-b^2$$; 11) $$1-25b^2$$; 12) $$9x^2-25y^2$$; 13) $$169c^2-100d^2$$; 14) $$121n^2-64m^2$$.