Proszę o pomoc !!! Zapisz wielomian w postaci sumy algebraicznej (2x-y)2 +12xy(x+y)-2y(3x+2y)2
Proszę o pomoc !!!
Zapisz wielomian w postaci sumy algebraicznej
(2x-y)2 +12xy(x+y)-2y(3x+2y)2
[latex](2x-y)^2 +12xy(x+y)-2y(3x+2y)^2=\\=4x^2-4xy+y^2+12x^2y+12xy^2-2y(9x^2+12xy+4y^2)=\\=4x^2-4xy+y^2+12x^2y+12xy^2-18x^2y-24xy^2-8y^3=\\= 4x^2-4xy+y^2-6x^2y-12xy^2 -8y^3[/latex]
[latex](a-b)^2=a^2-2ab+b^2 \ (a+b)^2=a^2+2ab+b^2 \ \ (2x-y)^2+12xy(x+y)-2y(3x+2y)^2= \ =4 x^{2} -4xy+y^2+12 x^{2} y+12xy^2-2y(9 x^{2} +12xy+4y^2)= \ =4 x^{2} -4xy+y^2+12 x^{2} y+12xy^2-18 x^{2} y-24xy^2-8y^3= \ =4 x^{2} -4xy+y^2-6 x^{2} y-12xy^2-8y^3 [/latex]