Question

Factorise x4+x2y2+y4

Answer 1

Given:-x^4+y^4+x^2×y^2
Now adding and subtracting 2x^2×y^2

x^4+y^4+x^2+y^2+2×x^2×y^2-2×x^2×y^2
Now
(x^2)^2+(y^2)^2+x^2+y^2+2×x^2×y^2-2×x^2×y^2
Now therefore we get
(x^2+y^2)^2+ x^2+y^2-2x^2×y^2=(x^2+y^2)^2+x^2+y^2-2×(xy)×(xy)=

(x^2+y^2)^2+(x-y)^2 × (xy)
Answer.


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