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Poziom C
Mistrz
doprowadź wyrażenie do najprostszej postaci​



Poziom C Mistrz Doprowadź Wyrażenie Do Najprostszej Postaci class=

Odpowiedź :

Domi

Poziom C

a)

[tex]8xy-(2x-3)(4y-5)=8xy-(8xy-10x-12y+15)=8xy-8xy+10x+12y-15=10x+12y-15[/tex]

b)

[tex](2x-3y)(5+x)+15(y-x)=10x+2x^{2} -15y-3xy+15y-15x=-5x+2x^{2} -3xy[/tex]

c)

[tex](5x-y)(2y-x)-11xy=10xy-5x^{2} -2y^{2} +xy-11xy=0-5x^{2} -2y^{2} =-5x^{2} -2y^{2}[/tex]\

d)

[tex]2(x+y)-(1-2x)(1+2y)=2x+2y-(1+2y-2x-4xy)=2x+2y-1-2y+2x+4xy=4x-1+4xy[/tex]

e)

[tex](4a-1)(2b+2)+2b(1-2a)=8ab+8a-2b-2+2b-4ab=4ab+8a-2[/tex]

f)

[tex](2a+b)(a-1)-(b-1)(a+2)=2a^{2} -2a+ab-b-(ab+2b-a-2)=2a^{2} -2a+ab-b-ab-2b+a+2=2a^{2}-a-3b+2[/tex]

Mistrz

a)

[tex](2s-4t-1)(t-s)-(s-2t-3)(t+s)=2st-2s^{2} -4t^{2} +4st-t+s-(st+s^{2}-2t^{2}-2st-3t-3s)=2st-2s^{2}-4t^{2}+4st-t+s-(-st+s^{2}-2t^{2}-3t-3s)=2st-2s^{2}-4t^{2}+4st-t+s+st-s^{2}+2t^{2}+3t+3s=7st-3s^{2}-2t^{2}+2t+4s[/tex]

b)

[tex](3m+1)(2m-1)(m-2)=(6m^{2}-3m+2m-1)(m-2)=(6m^{2} -m-1)(m-2)=6m^{3}-12m^{2}-m^{2}+2m-m+2=6m^{3}-13m^{2}+m+2[/tex]

c)

[tex]a-(a-1-b)(a+5)=a-(a^{2} +5a-a-5-ab-5b)=a-(a^{2}+4a-5-ab-5b)=a-a^{2}-4a+5+ab+5b=-3a-a^{2}+5+ab+5b[/tex]

d)

[tex]x^{2} y-(x-y^{2} -1)(x^{2} +2y-3)=x^{2} y-(x^{3}+2xy-3x-x^{2} y^{2}-2y^{3}+3y^{2}-x^{2} -2y+3)=x^{2} y-x^{3}-2xy+3x+x^{2} y^{2}+2y^{3}-3y^{2}+x^{2} +2y-3[/tex]

Krysia

[tex]a)\\\\ (2s-4t-1)(t-s)-(s-2t-3)(t+s)= \\\\=2ts-4t^2-t-2s^2+ 4st+s -(st-2t^2-3t+s^2-2st-3s)=\\\\= 2st -4t^2-t-2s^2+ 4st+s - st+2t^2+3t-s^2+2st+3s =\\\\= -3s^2+7st +4s-2t^2+2t =[/tex]

[tex]b)\\\\ (3m+1)(2m-1)(m-2)=(6m^2-3m+2m-1 )(m-2)=(6m^2- m -1 )(m-2)=\\\\=6m^3- m^2 -m -12m^2+ 2m + 2=6m^3- 13m^2 +m + 2\\\\c)\\\\a-(a-1-b)(a+5)=a-(a^2-a-ab+5a-5-5b)=\\\\=a- a^2+a+ab-5a+5+5b = -a^2+ab-3a+5b+5[/tex]

[tex]d)\\\\ x^2y-(x-y^2-1)(x^2+2y-3)=\\\\=x^2y-(x^3+2xy-3x-x^2y^2-2y^3+3y^2- x^2-2y+3)=\\\\ =x^2y- x^3-2xy+3x+x^2y^2+ 2y^3-3y^2+ x^2+2y-3=\\\\=- x^3+x^2y^2+x^2y+ x^2-2xy+3x+ 2y^3-3y^2+2y-3[/tex]

Inne Pytanie