Question

Zapisz w jak najprostszej postaci:

a) abc - (abc - (- xyz - (xyz - abc)))
b) s²t - (st² - (s²t - (st² - s²t)))
c) x²yz - (xy²z - (xyz² - (x²yz - xy²z)))

Answer 1

A) abc - (abc - (- xyz - (xyz - abc)))=
abc-(abc-(-xyz-xyz+abc))=
abc-(abc+xyz+xyz-abc)=
abc-abc-xyz-xyz+abc=abc-2xyz

b) s²t - (st² - (s²t - (st² - s²t)))
s²t-(st²-(s²t-st²+s²t))=
s²t-(st²-s²t+st²-s²t)=
s²t-st²+s²t-st²+s²t=3s²t-2st²

c) x²yz - (xy²z - (xyz² - (x²yz - xy²z)))
x²yz-(xy²z-(xyz²-x²yz+xy²z))=
x²yz-(xy²z-xyz²+x²yz-xy²z)=
x²yz-xy²z+xyz²-x²yz+xy²z=xyz²

Answer 2

Zapisz w jak najprostszej postaci:

a) abc - (abc - (- xyz - (xyz - abc)))=
abc - (abc - (- xyz - xyz+ abc))=abc - (abc - (- 2xyz + abc))=
abc - (abc + 2xyz - abc)=abc - abc - 2xyz + abc=
- 2xyz + abc

b) s²t - (st² - (s²t - (st² - s²t)))=s²t - (st² - s²t + st² - s²t)=
s²t - st² + s²t - st² + s²t=3 s²t - st²

c) x²yz - (xy²z - (xyz² - (x²yz - xy²z)))= x²yz - (xy²z - (xyz² - x²yz + xy²z))=
x²yz - (xy²z - xyz² + x²yz - xy²z)= x²yz - xy²z + xyz² - x²yz + xy²z= xyz²

Answer 3

A) abc - (abc - (- xyz - (xyz - abc))) = abc - (abc -(-xyz -xyz+abc))=
= abc-(abc+xyz+xyz-abc)=abc-abc-xyz-xyz+abc=abc-2xyz

b) s²t - (st² - (s²t - (st² - s²t))) = s²t - (st² - (s²t-st²+s²t))=
= s²t-(st²-s²t+st²-s²t)=s²t-st²+s²t-st²+s²t=3s²t-2st²

c) x²yz - (xy²z - (xyz² - (x²yz - xy²z))) = x²yz-(xy²z-(xyz²-x²yz+xy²z))=x²yz-(xy²-xyz²+x²yz-xy²z)=x²yz-xy²+xyz²-x²yz+xy²z=xyz²