Question

1)Вынесите общий множитель за скобки a) 3a^3b - 12a^2b + 6ab б) x (x - 1) + 2 (x - 1) 2) Разложите на множители а) xy + 3y + xz + 3z б) 25 - с^2 в) ab^2 - 2abc + ac^2 3) сократите дробь x^2 - xy ———— x^2 - y^2 4) Выполните действие (a - 2) (a + 2) - a (a - 1) 5) Решите уравнения a) (2x + 8)^2 = 0 б) x^2 - 4x = 0

Answer 1

Только во 2 в в) я хз как,но надеюсь,что этого хватит))))

Answer 2

A) 3a³b - 12a²b + 6ab = 3ab*(a² - 4a + 2)
б) x (x - 1) + 2 (x - 1) = (x - 1)(x + 2)


а) xy + 3y + xz + 3z = (xy + 3y) + (xz + 3z) = y*(x + 3) + z*(x + 3) = (x + 3)(y + z)
б) 25 - с² = (5 - c)(5 + c)
в) ab² - 2abc + ac² = a*(b² - 2bc + c²) = a*(b - c)²

x² - xy
———— = 
x² - y²

x*(x - y)                       
----------------    = (сокращаем (х - у) в числителе и знаменателе) = 
(x - y)(x + y) 

х
-------
х + у

(a - 2) (a + 2) - a (a - 1) = a² - 4 - a² + a = -4 + a

a) (2x + 8)² = 0,     x ≠ 4
4x² + 32x + 64 = 0
a = 4, b = 32, c = 64

по т. Виета: 
x1 + x2 = -b/a = -32/4 = -8
x1*x2 = c/a = 64/4 = 16

16 = (-4)*(-4)
-8 = -4 + (-4)

x1 = -4, x2 = -4

б) x² - 4x = 0
x*(x - 4) = 0
x = 0 или x - 4 = 0
x = 0,       x = 4

Answer 3

1. Вынесем общий множитель за скобки: а) 3a^3b - 12a^2b + 6ab = 3ab(a^2 - 4a + 2)

б) x(x - 1) + 2(x - 1) = (x - 1)(x + 2)

2. Разложим на множители: а) xy + 3y + xz + 3z = y(x + 3) + z(x + 3) = (x + 3)(y + z)

б) 25 - с^2 = (5 + c)(5 - c)

в) ab^2 - 2abc + ac^2 = ab(b - 2c) + ac^2 = ab(b - 2c) + ac(c) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0) = ab(b - 2c) + ac(c - 0