Madzia19952viz
Rozwiązane

1. Zapisz w postaci sumy algebraicznej :

a) (x+1)(x+2)(x+3) =

b) (x-2)(x+5)(2x-1) =

c) (x-4)(x+1)² =

d) (2x-4)²(x+2) =

2. Zapisz w jak najprostszej postaci :

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

b) (5k+n)(k-2n)-k(4k+n) =

c) (4y+3)(y-2)-2y(4-2y) =

d) -(3c-2)(c-1)-c(c-2) =

e) 2(3a²-1)-(a+2)(a+2) =

f) 5x²(x²+1)-(x²-2)(x²+3) =

Odpowiedź :

(x+1)(x+2)(x+3) =x do2 +2x + x +2[x+3]=
xdo3+2xdo2+x do2+2x+3x do 2 + 6x+3x+6xdo 3 +6x do 2 +5x + 6
(x-4)(x+1)²= (x-4)(x do 2 +1+2x)=
xdo3+x+2x do 2 -4xdo2-a-8x
1.
a) (x+1)(x+2)(x+3) =x2+2x+x+2+x2+3x+2x+6=x4+8x+8
b)(x-2)(x+5)(2x-1) = x2+5x-2x-10+2x2-x+10x-5=3x2+12x-10
c)(x-4)(x+1)² =(x-4)(x+1)(x+1) = x2-4x+x-4+x2+x+x+1=2x2-x-3
d)(2x-4)²(x+2) =(2x-4)(2x-4)(x+2) = 4x2-8x-8x+16+2x2+4x-4x-8=6x2-16x+8
2.
a) (x+1)(x-2)+(x+2)(x-1) =x2-2x+x-2+x2-x+2x-2=2x2-2
b) (5k+n)(k-2n)-k(4k+n) =5k2-10kn+kn-2n2-4k2-kn=-2n2+k2
c) (4y+3)(y-2)-2y(4-2y) = 4y2-8y+3y-6-8y+4y2=8y2-16y-6
d) -(3c-2)(c-1)-c(c-2) = -3c2+3c+2c-2-c2+2c=-4c2+7c-2
e) 2(3a²-1)-(a+2)(a+2) =6a2-2-a2-2a-2a-4=5a2-4a-6
f) 5x²(x²+1)-(x²-2)(x²+3) = 5x4+5x2-x4-3x2+2x2+6=4x4+4x2+6


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