Hva er parentesreglene?

Her skal du se på alle parentesreglene samlet sammen.

Regel

Parenteser

(a + b) (c + d) = a ⋅ c + a ⋅ d + b ⋅ c + b ⋅ d a + (c + d) = a + c + d a −(c + d) = a − c − d a ⋅(b + c) = a ⋅ b + a ⋅ c

(a + b) (c + d) = a ⋅ c + a ⋅ d + b ⋅ c + b ⋅ d a + (c + d) = a + c + d a −(c + d) = a − c − d a ⋅(b + c) = a ⋅ b + a ⋅ c

NB! Du må huske å skrive leddene i avtagende eller stigende rekkefølge. Da vil det se slik ut:

2x3 − 4x2 + 3 eller  − 1 + 3x − 2x2 + x3

Eksempel 1

Regn ut x + (−2x + 5)

x + (−2x + 5) = x − 2x + 5 = −x + 5

Eksempel 2

Regn ut 4 −(12 − 3x2)

4 −(12 − 3x2) = 4 − 12 + 3x2 = 3x2 − 8

Eksempel 3

Regn ut −4x2 (2 − x)

−4x2 (2 − x) = −8x2 + 4x3 = 4x3 − 8x2

Eksempel 4

Regn ut (x + 1) (x − 2)

(x + 1) (x − 2) = x2 − 2x + x − 2 = x2 − x − 2

(x + 1) (x − 2) = x2 − 2x + x − 2 = x2 − x − 2

Eksempel 5

Regn ut (3x2 + y) (2 − x)

(3x2 + y) (2 − x) = 6x2 − 3x3 + 2y − xy = −3x3 + 6x2 − xy + 2y

Eksempel 6

Regn ut (2x + 3) (4x − 5)

(2x + 3) (4x − 5) = 2x ⋅ 4x + 2x ⋅(−5) + 3 ⋅ 4x + 3 ⋅(−5) = 8x2 + (−10x) + 12x − 15 = 8x2 + 2x − 15

(2x + 3) (4x − 5) = 2x ⋅ 4x + 2x ⋅(−5) + 3 ⋅ 4x + 3 ⋅(−5) = 8x2 + (−10x) + 12x − 15 = 8x2 + 2x − 15