What is factor x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4 ?

The solution to factor x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4 is (x^2+y^2+xy)(x^2+y^2-xy)(x+1)

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factor x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4

factor

x^{5} + x^{3} y^{2} + x y^{4} + x^{4} + x^{2} y^{2} + y^{4}

(x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y) (x + 1)

Solution steps

x^{5} + x^{3} y^{2} + x y^{4} + x^{4} + x^{2} y^{2} + y^{4}

= (x^{5} + x^{3} y^{2} + x y^{4}) + (x^{4} + x^{2} y^{2} + y^{4})

Factor out

x

from

x^{5} + x^{3} y^{2} + x y^{4} : x (x^{4} + x^{2} y^{2} + y^{4})

= x (x^{4} + x^{2} y^{2} + y^{4}) + (x^{4} + x^{2} y^{2} + y^{4})

Factor out common term

(x^{4} + x^{2} y^{2} + y^{4}) : (x^{4} + x^{2} y^{2} + y^{4}) (x + 1)

= (x^{4} + x^{2} y^{2} + y^{4}) (x + 1)

Factor

x^{4} + x^{2} y^{2} + y^{4} : (x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y)

= (x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y) (x + 1)

\frac{6 \cdot 3}{6 + 3}

(x + 2)^{2} = 16

(3 - 4 i) (- 3 + 2 i)

2 (x + 1)^{2} - 6 (x + 1) + 4

5 x^{\frac{14}{5}} - 48 x^{\frac{9}{5}} + 64 x^{\frac{4}{5}}

What is factor x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4 ?
The solution to factor x^5+x^3y^2+xy^4+x^4+x^2y^2+y^4 is (x^2+y^2+xy)(x^2+y^2-xy)(x+1)