Question

factorize - (x⁴+x²y²+y⁴)​

Answer 1

Answer:

(x^2+xy+y^2)(x^2--xy+y^2)

Answer 2

Answer:

thanks bro

Step-by-step explanation:

Solution x^4 + x^2y^2 + y^4

= (x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2= (x^2 +xy + y^2)(x^2 -xy + y^2)

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2= (x^2 +xy + y^2)(x^2 -xy + y^2)= (x^2 +xy +xy+ y^2 - xy)(x^2 -xy -xy+ y^2 + xy)

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2= (x^2 +xy + y^2)(x^2 -xy + y^2)= (x^2 +xy +xy+ y^2 - xy)(x^2 -xy -xy+ y^2 + xy)= [(x^2+2xy+y^2)-xy][(x^2-2xy+y^2)+xy]

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2= (x^2 +xy + y^2)(x^2 -xy + y^2)= (x^2 +xy +xy+ y^2 - xy)(x^2 -xy -xy+ y^2 + xy)= [(x^2+2xy+y^2)-xy][(x^2-2xy+y^2)+xy]= [(x+y)^2-xy][(x-y)^2+xy]

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2= (x^2 +xy + y^2)(x^2 -xy + y^2)= (x^2 +xy +xy+ y^2 - xy)(x^2 -xy -xy+ y^2 + xy)= [(x^2+2xy+y^2)-xy][(x^2-2xy+y^2)+xy]= [(x+y)^2-xy][(x-y)^2+xy]= [(x+y)+ √(xy)][(x+y)- √(xy)][(x-y)^2+xy]

(x^4 + x^2y^2 + x^2y^2 + y^4) - x^2y^2= (x^4 + 2x^2y^2 + y^4) - x^2y^2= (x^2 + y^2)^2 - (xy)^2= (x^2 +xy + y^2)(x^2 -xy + y^2)= (x^2 +xy +xy+ y^2 - xy)(x^2 -xy -xy+ y^2 + xy)= [(x^2+2xy+y^2)-xy][(x^2-2xy+y^2)+xy]= [(x+y)^2-xy][(x-y)^2+xy]= [(x+y)+ √(xy)][(x+y)- √(xy)][(x-y)^2+xy]= [(x+y)+ √(xy)]*[(x+y)- √(xy)]*[(x-y)^2+ i√(xy)]*[(x-y)^2- i√(xy)]