Răspuns:
Explicație pas cu pas:
1.
a)
3 ᵒ (-2) = 3·(-2) + 2·3 + 2·(-2) + 2 = - 6 + 6 - 4 + 2 = - 2
b)
x ᵒ x = x² + 2x + 2x + 2 = x
x² + 2x + 2x - x + 2 = 0
x² + 2x + x + 2 = 0
x(x + 2 ) + (x + 2) = 0
(x + 2 )(x + 1 ) = 0
x + 2 = 0 ⇒ x = -2
x + 1 = 0 ⇒ x = -1
c)
x ᵒ y = xy + 2x + 2x + 2 = xy + 2x + 2y + 4 - 2 = x(y + 2 ) + (y + 2) - 2 = (y + 2)(x + 2) -2 = (x + 2)(y + 2) - 2
d)
x ᵒ (-2) = x·(-2) + 2x + 2·(-2) + 2 = - 2x + 2x - 4 + 2 = - 2
2.
a)
1 ᵒ 2015 = -1·2015 + 1 + 2015 = -2015 + 1 + 2015 = 1
b)
x ᵒ y = -xy + x + y = -xy + x + y - 1 + 1 = -(xy - x - y + 1 ) + 1 = -[x(y - 1) - (y - 1)] + 1 = -(y - 1)(x - 1) + 1 = -(x - 1)(y - 1) + 1
