Question

1 zapisz w jak najprostrzej postaci

(x+1)(x-2)+(x+2)(x-1)

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

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

Answer 1

(x+1)(x-2)+(x+2)(x-1)= x^2-2x+x-2+x^2-x+2x-2= 2x^2-4= 2(x^2-2)=

=2(x-pierwiastek z 2)(x+pierwiastek z 2)

 

(5k+n) (k-2n)-k(4k+n)= 5k^2-10kn+kn-2n^2-4k^2-kn= k^2-10k-2n^2

 

(4y+3)(y-2)-2y(4-2y)=4y^2-8y+3y-6-8y-4y^2= 8y^2-13y-6

8^2-13y-6=0

delta=168-4*8*(-6)

delta=169+192=361

pierwiastek z delta= 19

 

y1= (13+19)/18=32/16=2

y2=(13-19)/18=-3/8

 

 

8(y-2)(y+3/8)