Упростите выражение и найдите его значение:
а) $(5a - 10)^2 - (3a - 8)^2 + 132a$ при a = −6;
б) $(3p - 8)^2 + (4p + 6)^2 + 100p$ при p = −2;
в) $(5b - 3)^2 + (12b - 4)^2 - 4b$ при b = −1;
г) $(13 - 5m)^2 - (12 - 4m)^2 + 4m$ при $m = -\frac{2}{3}$.
$(5a - 10)^2 - (3a - 8)^2 + 132a = 25a^2 - 100a + 100 - (9a^2 - 48a + 64) + 132a = 25a^2 - 100a + 100 - 9a^2 + 48a - 64 + 132a = 16a^2 + 80a + 36$
при a = −6:
$16 * (-6)^2 + 80 * (-6) + 36 = 16 * 36 - 480 + 36 = 576 - 480 + 36 = 132$
$(3p - 8)^2 + (4p + 6)^2 + 100p = 9p^2 - 48p + 64 + 16p^2 + 48p + 36 + 100p = 25p^2 + 100p + 100 = (5p + 10)^2$
при p = −2:
$(5 * (-2) + 10)^2 = (-10 + 10)^2 = 0^2 = 0$
$(5b - 3)^2 + (12b - 4)^2 - 4b = 25b^2 - 30b + 9 + 144b^2 - 96b + 16 - 4b = 169b^2 - 130b + 25 = (13b - 5)^2$
при b = −1:
$(13 * (-1) - 5)^2 = (-13 - 5)^2 = (-18)^2 = 324$
$(13 - 5m)^2 - (12 - 4m)^2 + 4m = 169 - 130m + 25m^2 - (144 - 96m + 16m^2) + 4m = 169 - 130m + 25m^2 - 144 + 96m - 16m^2 + 4m = 9m^2 - 30m + 25 = (3m - 5)^2$
при $m = -\frac{2}{3}$:
$(3m - 5)^2 = (3 * (-\frac{2}{3}) - 5)^2 = (-2 - 5)^2 = (-7)^2 = 49$
Пожаулйста, оцените решение
