Question

factorise x^4 + y^4 + x^2 + y^2
do fast it's very urgent

Answer 1

[tex]x^4+y^4+x^2+y^2 [/tex]
=$(x+y)^2-2xy + (x+y)^4-(4x^3y+6x^2y^2+4xy^3)$
=$(x+y)^4+(x+y)^2-2xy-2xy(2x^2+3xy+2y^2)$
=$(x+y)^2((x+y)^2+1) -2xy(2x^2+3xy+2y^2+1)$
=[tex](x^2+2xy+y^2)(x^2+2xy+y^2+1) - 2xy(x^2+2xy+y^2+1) [/tex]
=$(x^2+2xy+y^2-2xy)(x^2+y^2+2xy+1)$
=$(x^2+y^2)(x^2+2xy+y^2+1)$