Упр.76 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

1) (8x^2-12x+4)-(2x^2+5x-2);
2) (11+2x)+(-x^2+12x-35)4;
3) (7a^2-3a+6)-(-8a+2a^3+5);
4) (14xy-2y^2+13x^2 )-(-16y^2-5xy+4x^2 );
5) (18a^2 b+9ab-2ab^2 )+(4ab+2ab^2 );
6) (3/14 x^2 y^3-5/8 x^2 y)-(-3/12 x^2 y-4/35 x^2 y^3 ).

1. $$\begin{aligned}
   (8x^2-12x+4)-(2x^2+5x-2) &= 8x^2-12x+4-2x^2-5x+2 \\
   &= 6x^2-17x+6.
   \end{aligned}$$

2. $$\begin{aligned}
   (11+2x)+(-x^2+12x-35) &= 11+2x-x^2+12x-35 \\
   &= -x^2+14x-24.
   \end{aligned}$$

3. $$\begin{aligned}
   (7a^2-3a+6)-(-8a+2a^3+5) &= 7a^2-3a+6+8a-2a^3-5 \\
   &= -2a^3+7a^2+5a+1.
   \end{aligned}$$

4. $$\begin{aligned}
   (14xy-2y^2+13x^2)-(-16y^2-5xy+4x^2) &= 14xy-2y^2+13x^2+16y^2+5xy-4x^2 \\
   &= 9x^2+19xy+14y^2.
   \end{aligned}$$

5. $$\begin{aligned}
   (18a^2b+9ab-2ab^2)+(4ab+2ab^2) &= 18a^2b+9ab-2ab^2+4ab+2ab^2 \\
   &= 18a^2b+13ab.
   \end{aligned}$$

6. $$\begin{aligned}
   \left(\frac{3}{14}x^2y^3-\frac{5}{8}x^2y\right)-\left(-\frac{3}{12}x^2y-\frac{4}{35}x^2y^3\right)
   &= \frac{3}{14}x^2y^3-\frac{5}{8}x^2y+\frac{3}{12}x^2y+\frac{4}{35}x^2y^3 \\
   &= \left(\frac{3}{14}+\frac{4}{35}\right)x^2y^3+\left(\frac{3}{12}-\frac{5}{8}\right)x^2y \\
   &= \frac{23}{70}x^2y^3-\frac{9}{24}x^2y \\
   &= \frac{23}{70}x^2y^3-\frac{3}{8}x^2y.
   \end{aligned}$$

Ответ

$$1)\ 6x^2-17x+6;\quad 2)\ -x^2+14x-24;\quad 3)\ -2a^3+7a^2+5a+1;$$
$$4)\ 9x^2+19xy+14y^2;\quad 5)\ 18a^2b+13ab;\quad 6)\ \frac{23}{70}x^2y^3-\frac{3}{8}x^2y.$$