What is factor x^4+2x^2y+y^2 ?

The solution to factor x^4+2x^2y+y^2 is (x^2+y)^2

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factor x^4+2x^2y+y^2

factor

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

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

Solution steps

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

Break the expression into groups

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

Factor out

x^{2}

from

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

Factor out

y

from

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

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

Factor out common term

x^{2} + y

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

Apply exponent rule:

aa = a^{2}

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

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

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What is factor x^4+2x^2y+y^2 ?
The solution to factor x^4+2x^2y+y^2 is (x^2+y)^2