Question

Решите, пожалуйста, примеры по теме:
"Разложение многочленов на множители с помощью формул сокращённого умножения"
P.S. надо только отмеченные (30.9,12,14,16,18,19,21,23 все под пунктами В!!!)

Answer 1

$30.9 \ 36a^2 - 25 = 0\\\\ (6a)^2 - 5^2 = (6a - 5)(6a + 5) = 0\\\\ 6a \mp 5 = 0, \ 6a = \pm 5 , \ \boxed{a = \pm\frac{5}{6}}\\\\ 30.12 \ 512b^3 - 125 = (8b)^3 - 5^3 = \boxed{(8b - 5)(64b^2 + 40b + 25)}\\\\ 30.14 \ 216x^3 - y^3 = (6x)^3 - y^3 = \boxed{(6x - y)(36x^2 + 6xy + y^2)}$

$30.16 \ 1 - 2b + b^2 = 1 - b - b + b^2 =\\\\ = (1- b) - b(1 - b) = (1-b)(1-b) = \boxed{(1 - b)^2}\\\\ 30.18 \ x^2 - 14xy + 49y^2 = x^2 - 7xy - 7xy + 49y^2 = \\\\ = x(x - 7y) - 7y(x - 7y) = (x - 7y)(x- 7y) = \boxed{(x - 7y)^2}\\\\ 30.19 \ 4m^2 - 28mn + 49n^2 = 4m^2 - 14mn - 14mn + 49n^2 = \\\\ = 2m(2m - 7n) - 7n(2m - 7n) = (2m - 7n)(2m - 7n) = \boxed{(2m - 7n)^2}$

$30.21 \ 625 - (n + 12)^2 = 25^2 - (n + 12)^2 = \\\\ = (25 - n - 12)(25 + n + 12) = \boxed{(13 - n)(37 + n)}\\\\ 30.23 \ (m + 10)^2 - (n - 12)^2 = (m + 10 - n + 12)(m + 10 + n - 12) = \\\\ = \boxed{(m - n + 22)(m + n - 2)}$