DZiał wielomiany oblicz :a)(x2-x+1)2-(x2+x+1)2 =  wynik ma wyjść (-4x3-4x)b) (3x2-x+2)2- (3x2+x+2)2= wynik ma wyjść (-12x3-8x)c)(x2+x)2+(3x2+1)2=  wynik ma wyjść (10x4+2x3+7x2+1)x2-oznacz x do potęgi 2

[latex]a)\ (x^2-x+1)^2-(x^2+x+1)^2=[x(x-1)+1]^2-[x(x+1)+1]^2=\ x^2(x-1)^2+2x(x-1)+1-[x^2(x+1)^2+2x(x+1)+1]=\ x^2(x^2-2x+1)+2x^2-2x+1-[x^2(x^2+2x+1)+2x^2+2x+1]=\ x^4-2x^3+x^2+2x^2-2x+1-(x^4+2x^3+x^2+2x^2+2x+1)=\ x^4-2x^3+3x^2-2x+1-x^4-2x^3-3x^2-2x-1=-4x^3-4x\[/latex] [latex]b)\(3x^2-x+2)^2-(3x^2+x+2)^2=[x(3x-1)+2]^2-[x(3x+1)+2]^2=\ x^2(3x-1)^2+4x(3x-1)+4-[x^2(3x+1)^2+4x(3x+1)+4]=\ [/latex] [latex]= x^2(9x^2-6x+1)+12x^2-4x-4-\ -[x^2(9x^2+6x+1)+12x^2+4x+4]=\9x^4-6x^3+x^2+12x^2-4x+4-(9x^4+6x^3+x^2+12x^2+4x+4)=\ 9x^4-6x^3+13x^2-4x+4-9x^4-6x^3-13x^2-4x-4=12x^3-8x\ [/latex] [latex]c)\(x^2+x)^2+(3x^2+1)^2=x^4+2x^3+x^2+9x^4+6x^2+1=\ 10x^4+2x^3+7x^2+1[/latex]