Найдите значение выражения $21a^2b - 4b - 12a + 7ab^2$, если:
а) $a = -\frac{1}{3}; b = 2$;
б) $a = 4; b = \frac{1}{7}$;
в) $a = 1\frac{1}{7}; b = 0,5$;
г) $a = -\frac{2}{3}; b = 3$.
$21a^2b - 4b - 12a + 7ab^2 = (21a^2b + 7ab^2) - (12a + 4b) = 7ab(3a + b) - 4(3a + b) = (3a + b)(7ab - 4)$
если $a = -\frac{1}{3}; b = 2$:
$(3 * (-\frac{1}{3}) + 2)(7 * (-\frac{1}{3}) * 2 - 4) = (-1 + 2)(-\frac{14}{3} - 4) = -4\frac{2}{3} - 4 = -8\frac{2}{3}$
Ответ: $-8\frac{2}{3}$
$21a^2b - 4b - 12a + 7ab^2 = (21a^2b + 7ab^2) - (12a + 4b) = 7ab(3a + b) - 4(3a + b) = (3a + b)(7ab - 4)$
если $a = 4; b = \frac{1}{7}$:
$(3a + b)(7ab - 4) = (3 * 4 + \frac{1}{7})(7 * 4 * \frac{1}{7} - 4) = (12 + \frac{1}{7})(28 * \frac{1}{7} - 4) = 12\frac{1}{7} * (4 - 4) = 12\frac{1}{7} * 0 = 0$
Ответ: 0
$21a^2b - 4b - 12a + 7ab^2 = (21a^2b + 7ab^2) - (12a + 4b) = 7ab(3a + b) - 4(3a + b) = (3a + b)(7ab - 4)$
если $a = 1\frac{1}{7}; b = 0,5$:
$(3a + b)(7ab - 4) = (3 * 1\frac{1}{7} + 0,5)(7 * 1\frac{1}{7} * 0,5 - 4) = (3 * \frac{8}{7} + \frac{1}{2})(7 * \frac{8}{7} * \frac{1}{2} - 4) = (\frac{24}{7} + \frac{1}{2})(4 - 4) = (\frac{24}{7} + \frac{1}{2}) * 0 = 0$
Ответ: 0
$21a^2b - 4b - 12a + 7ab^2 = (21a^2b + 7ab^2) - (12a + 4b) = 7ab(3a + b) - 4(3a + b) = (3a + b)(7ab - 4)$
$a = -\frac{2}{3}; b = 3$:
$(3 * (-\frac{2}{3}) + 3)(7 * (-\frac{2}{3}) * 3 - 4) = (-2 + 3)(7 * (-2) - 4) = -14 - 4 = -18$
Ответ: −18
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