Упр.14.7 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

Задача

14.7. Вычислите:
1) $$3{,}74^2+3{,}74\cdot2{,}26-3{,}74\cdot1{,}24-2{,}26\cdot1{,}24$$;
2) $$58{,}7\cdot1{,}2+36\cdot3{,}52-34{,}7\cdot1{,}2-2{,}32\cdot36$$;
3) $$2\frac{4}{9}\cdot3\frac{2}{7}+1\frac{5}{7}\cdot2{,}8+2\frac{5}{9}\cdot3\frac{2}{7}+1\frac{5}{7}\cdot2{,}2$$.

Подробный ответ

1) $$3{,}74^2+3{,}74\cdot 2{,}26-3{,}74\cdot 1{,}24-2{,}26\cdot 1{,}24$$

$$=3{,}74(3{,}74+2{,}26)-1{,}24(3{,}74+2{,}26)$$
$$=(3{,}74+2{,}26)(3{,}74-1{,}24)$$
$$=6\cdot 2{,}5=15.$$

2) $$58{,}7\cdot 1{,}2+36\cdot 3{,}52-34{,}7\cdot 1{,}2-2{,}32\cdot 36$$

$$=(58{,}7\cdot 1{,}2-34{,}7\cdot 1{,}2)+(36\cdot 3{,}52-2{,}32\cdot 36)$$
$$=1{,}2(58{,}7-34{,}7)+36(3{,}52-2{,}32)$$
$$=1{,}2\cdot 24+36\cdot 1{,}2$$
$$=1{,}2(24+36)=1{,}2\cdot 60=72.$$

3) $$2\frac{4}{9}\cdot 3\frac{2}{7}+1\frac{5}{7}\cdot 2{,}8+2\frac{5}{9}\cdot 3\frac{2}{7}+1\frac{5}{7}\cdot 2{,}2$$

$$=\left(2\frac{4}{9}\cdot 3\frac{2}{7}+2\frac{5}{9}\cdot 3\frac{2}{7}\right)+\left(1\frac{5}{7}\cdot 2{,}8+1\frac{5}{7}\cdot 2{,}2\right)$$
$$=3\frac{2}{7}\left(2\frac{4}{9}+2\frac{5}{9}\right)+1\frac{5}{7}(2{,}8+2{,}2)$$
$$=3\frac{2}{7}\cdot 5+1\frac{5}{7}\cdot 5$$
$$=5\left(3\frac{2}{7}+1\frac{5}{7}\right)=5\cdot 5=25.$$