Rozwiązane

Wyrażenia algebraiczne.
Zapisz w jak najprostrzej postaci :

a)(x+1)(x-2)+(x+2)(x-1=
b)(5k+2)(k-2n)-k(4k+n)=
c)(4y+3)(y-2)-2y(4-2y)=
d)-3(3c-2)(c-1)-c(c-2)=
e)2(3a²-1)-(a+2)(a+2)=
f)5x²(x²+1)-(x²-2(x²+3)=

proszę napisać tak bym mogła podkreślić wyrazy podobne i wynik podać dopiero po redukcji :)
z góry dzieki ;**



Odpowiedź :

N00nst00p
a)(x+1)(x-2)+(x+2)(x-1)=
= x²-2x+x-2+x²-x+2x-2=
= 2x²-4

b)(5k+2)(k-2n)-k(4k+n)=
= 5k²-10kn+2k-4n-4k²-kn=
= k²-11kn-2n

c)(4y+3)(y-2)-2y(4-2y)=
= 4y²-8y+3y-6-8y+4y=
= 4y²-16y+7y-6

d)-3(3c-2)(c-1)-c(c-2)=
= -3(3c²-3c-2c+2)-c²+2c=
= -9c²+9c+6-6-c²+2c=
= -10c²+11c

e)2(3a²-1)-(a+2)(a+2)=
= 6a²-2-(a²+2a+2a+4=
= 6a²-2-a²-2a-2a-4=
= 5a²-4a-6

f)5x²(x²+1)-(x²-2)(x²+3)=
= 5x⁴+5x²- (x⁴+3x²-2x²-6)=
= 5x⁴+5x²-x⁴-3x²+2x²+6=
= 4x⁴+4x²+6
Szpagatka
a) (x+1)(x-2)+(x+2)(x-1) = x²-2x+x-2+x²-x+2x-2 = 2x²-4 = 2(x²-2)
b) (5k+2)(k-2n)-k(4k+n) = 5k²-10kn+2k-4n-4k²-kn = k²-9kn+2k-4n
c) (4y+3)(y-2)-2y(4-2y) = 4y²-8y+3y-6-8y+4y² = 8y²-13y-6
6d) -3(3c-2)(c-1)-c(c-2) = -3(3c²-3c-2c+2)-c²+2c = -9c²+9c+6c-c²+2c = -10c²+17c
e) 2(3a²-1)-(a+2)(a+2) = 6a²-2-(a²+2a+2a+4) = 6a²-2-a²-2a-2a-4 = 5a²-4a-6
f) 5x²(x²+1)-(x²-2)(x²+3) = 5x⁴+5x²-(x⁴+3x²-2x²-6) = 5x⁴+5x²-x⁴+2x²+2x²+6 = 4x⁴+9x²+6

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