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

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

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

factor

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

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

Solution steps

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

Break the expression into groups

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

Factor out

x^{2}

from

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

Factor out

y^{2}

from

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

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

Factor out common term

x^{2} + y^{2}

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

Apply exponent rule:

aa = a^{2}

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

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

3 x + 1 = 0

(\frac{13}{3})^{2}

14 x^{2} y^{5} (11 x^{5} y^{5})

- \frac{1}{8} + \frac{3}{4}

4 n^{2} - 16 n - 84

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