Упр.76 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

Упростите выражение:

1) $$(6x^2 — 7x + 4) — (4x^2 — 4x + 18);$$
2) $$(3x + 9) + (-x^2 — 15x — 40);$$
3) $$(10a^2 — 6a + 5) — (-11a + a^3 + 6);$$
4) $$(13xy — 11x^2 + 10y^2) — (-15x^2 + 10xy — 15y^2);$$
5) $$(14ab^2 — 17ab + 5a^2b) + (20ab — 14a^2b);$$
6) $$\left(\frac{7}{8}x^3y^2 — \frac{5}{6}xy^2\right) — \left(-\frac{7}{12}xy^2 + \frac{5}{12}x^3y^2\right).$$

1. $$\begin{aligned} (6x^2-7x+4)-(4x^2-4x+18) &= 6x^2-7x+4-4x^2+4x-18 \\ &= 2x^2-3x-14. \end{aligned}$$
2. $$\begin{aligned} (3x+9)+(-x^2-15x-40) &= 3x+9-x^2-15x-40 \\ &= -x^2-12x-31. \end{aligned}$$
3. $$\begin{aligned} (10a^2-6a+5)-(-11a+a^3+6) &= 10a^2-6a+5+11a-a^3-6 \\ &= -a^3+10a^2+5a-1. \end{aligned}$$
4. $$\begin{aligned} (13xy-11x^2+10y^2)-(-15x^2+10xy-15y^2) &= 13xy-11x^2+10y^2+15x^2-10xy+15y^2 \\ &= 4x^2+3xy+25y^2. \end{aligned}$$
5. $$\begin{aligned} (14ab^2-17ab+5a^2b)+(20ab-14a^2b) &= 14ab^2-17ab+5a^2b+20ab-14a^2b \\ &= 14ab^2+3ab-9a^2b. \end{aligned}$$
6. $$\begin{aligned} \left(\frac{7}{8}x^3y^2-\frac{5}{6}xy^2\right)-\left(-\frac{7}{12}xy^2+\frac{5}{12}x^3y^2\right) &= \frac{7}{8}x^3y^2-\frac{5}{6}xy^2+\frac{7}{12}xy^2-\frac{5}{12}x^3y^2 \\ &= \left(\frac{7}{8}-\frac{5}{12}\right)x^3y^2+\left(-\frac{5}{6}+\frac{7}{12}\right)xy^2 \\ &= \frac{11}{24}x^3y^2-\frac{1}{4}xy^2. \end{aligned}$$